2025Activity reportProject-TeamPASTA
RNSR: 202023683K- Research center Inria Centre at Université de Lorraine
- In partnership with:Université de Lorraine, CNRS
- Team name: Space-time random processes and applications
- In collaboration with:Institut Elie Cartan de Lorraine (IECL)
Creation of the Project-Team: 2020 December 01
Each year, Inria research teams publish an Activity Report presenting their work and results over the reporting period. These reports follow a common structure, with some optional sections depending on the specific team. They typically begin by outlining the overall objectives and research programme, including the main research themes, goals, and methodological approaches. They also describe the application domains targeted by the team, highlighting the scientific or societal contexts in which their work is situated.
The reports then present the highlights of the year, covering major scientific achievements, software developments, or teaching contributions. When relevant, they include sections on software, platforms, and open data, detailing the tools developed and how they are shared. A substantial part is dedicated to new results, where scientific contributions are described in detail, often with subsections specifying participants and associated keywords.
Finally, the Activity Report addresses funding, contracts, partnerships, and collaborations at various levels, from industrial agreements to international cooperations. It also covers dissemination and teaching activities, such as participation in scientific events, outreach, and supervision. The document concludes with a presentation of scientific production, including major publications and those produced during the year.
Keywords
Computer Science and Digital Science
- A6.2.2. Numerical probability
- A6.2.3. Probabilistic methods
- A6.2.4. Statistical methods
- A6.3.3. Data processing
Other Research Topics and Application Domains
- B3.3.1. Earth and subsoil
- B3.4.1. Natural risks
- B9.6.3. Economy, Finance
- B9.6.10. Digital humanities
- B9.11. Risk management
- B9.11.1. Environmental risks
- B9.11.2. Financial risks
1 Team members, visitors, external collaborators
Research Scientists
- Madalina Deaconu [Team leader, INRIA, Senior Researcher, HDR]
- Antoine Lejay [INRIA, Senior Researcher, HDR]
Faculty Members
- Lionel Lenôtre [UHA, Associate Professor Delegation, from Sep 2025]
- Sara Mazzonetto [UL, Associate Professor, from Sep 2025]
- Sara Mazzonetto [UL, Associate Professor Delegation, from Mar 2025 until Aug 2025]
- Sara Mazzonetto [UL, Associate Professor, until Feb 2025]
- Pascal Moyal [UL, Professor, HDR]
- Catherine Roth [UHA, Associate Professor Delegation, until Aug 2025]
- Radu Stoica [UL, Professor, HDR]
PhD Students
- Lorenzo Agabiti [SORBONNE UNIVERSITE]
- Julia Budzinski [INRIA]
- Nathan Gillot [UL, ATER, from Oct 2025]
- Nathan Gillot [UL, until Sep 2025]
- Freja Amalie Noerby [UNIV COPENHAGUE, from Oct 2025]
- Saïd Toubra [CNRS]
Technical Staff
- Amélie Ferstler [INRIA, Engineer, until Nov 2025]
Interns and Apprentices
- Kevi Aliu [INRIA, Intern, from Apr 2025 until Sep 2025]
- Swann Cordier [Ecole des Mines de Nancy, Intern, until May 2025]
- Youcef Dermeche [Ecole des Mines de Nancy, Intern, from Aug 2025]
Administrative Assistants
- Marine Dufourmantelle [INRIA]
- Ouiza Herbi [INRIA]
External Collaborator
- Lionel Lenôtre [UHA, until Aug 2025]
2 Overall objectives
PASTA is a joint research team between Inria Research Center at Université de Lorraine, CNRS and Université de Lorraine, located at Institut Élie Cartan de Lorraine.
PASTA aims to construct and develop new methods and techniques by promoting and interweaving stochastic modeling and statistical tools to integrate, analyze and enhance real data.
The specificity and the identity of PASTA are:
- the embedding of spatio-temporal statistics and stochastic process analysis into models to tackle challenging complex problems that require new mathematical techniques, by combining the strengths of these two scientific domains;
- to deal with the increase of available data, the construction of suitable models which incorporate prior knowledge on their spatio-temporal structures. For this, we design and analyze simulation and inference techniques, and focus on the interpretation, the validation and the explanation of both the models and the algorithms, in close interaction with practitioners.
The leading direction of our research is to develop the topic of data enriched spatio-temporal stochastic models, through a mathematical perspective. Specifically, we jointly leverage major tools of probability and statistics: data analysis and the analytical study of stochastic processes. We aim at exploring the three different aspects, namely: shape, time and environment, of the same phenomenon. These mathematical methodologies will be intended for solving real-life problems through inter-disciplinary and industrial partnerships.
3 Research program
Our research program develops three interwoven axes:
- stochastic modeling,
- simulation algorithms,
- inference and data analysis.
In particular, we are interested in the evolution of stochastic dynamical systems evolving in intricate configuration spaces. These configuration spaces could be spatial positions, graphs, physical spaces with singularities, space of measures, space of chemical compounds, and so on.
When facing a new modeling question, we have to construct the appropriate class of models among what we call the meta-models. Meta-models and then models are selected according to the properties to be simulated or inferred as well as the objectives to be reached. Among other examples of such meta-models which we regularly use, let us mention Markov processes (diffusion, jump, branching processes), Gibbs measures, and random graphs. On these topics, the team has an intensive research experience from different perspectives.
Finding the balance between usability, interpretability and realism is our first guide. This is the keystone in modeling, and the main difference with black-box approaches in machine learning. Our second guide is to study the related mathematical issues in modeling, simulation and inference. Models are sources of interesting open mathematical questions. We are eager to expand the “capacity” of the models by exploring their mathematical properties, providing simulation algorithms or proposing more efficient ones, as well as new inference procedures with statistical guarantees.
To study and apply the class of stochastic models we have to handle the following questions:
- modeling: identifying the quantities of interest, the nature of the randomness, the nature of their dynamical evolution and the useful variables. Finally, we have to specify the statistical properties of the stochastic process at stake: Markov or long-range dependency, time/space-stationarity or transience, integrability, and so on.
- stochastic analysis: providing rigorous tools to study the model and controlling its characteristics in steady state or in transient regime (hitting times of a given state, rare events, etc.).
- simulation: this is an important tool to understand the behavior of random systems, but also to solve deterministic problems such as Partial Differential Equations or, in inference, to overcome limitations due to intractable quantities. We then consider open and challenging problems such as considering singular diffusion problems, accurate hitting times simulations, simulation of complex stochastic processes as well as extending perfect simulation and adapted MCMC (Monte Carlo Markov Chain) algorithms. Rigorously proving the amenability of such algorithms for their use in statistical inference is important for their practical applications.
- inference: specifying tools to evaluate the model under study in a parametric or non-parametric setting in the appropriate context (frequentist or Bayesian), developing the suitable numerical methods (stochastic algorithms, MCMC) and controlling the quality of the estimation.
4 Application domains
Our main application domains are: economy, geophysics, medicine, astronomy and digital humanities.
We aim at providing new tools regarding the modeling, simulation and inference of spatio-temporal stochastic processes and other dynamical random systems living in large state spaces. As such, there are many application domains which we consider.
In particular, we have partnerships with practitioners in: geophysics, insurance, cosmology, healthcare systems, and telecom networks.
We detail below our actions in the most representative application domains.
4.1 Geophysics
Geophysics is a domain which requires the application of a broad range of mathematical tools related to probability and statistics while more and more data are collected. There are several directions in which we develop our methodology in relation with practitioners in the field:
- Avalanches (snow or rock) present intricate dynamical properties, with a wide variety of behaviors that largely depend on their environments. To model such phenomena, we apply tools from fragmentation theory, stochastic calculus, partial differential equations and branching processes. Our techniques and developments differ from existing approaches (as we are considering the behavior at the microscopic scale and we are following the evolution of a typical particle) and introduce innovative solutions. Thus, the approach we consider is new and paves the way to considering and constructing rigorous mathematical models and simulation procedures able to reproduce and control the real phenomenon by introducing more and more issues in the models.
- Understanding the behavior of subsurface and surface fluids is a major challenge in geophysics. We deal with two main axes: (1) using tools for spatial Bayesian statistics which consists in detecting the sources of the various components of fluids from their hydrogeochemical data, and (2) developing the suitable methodological and numerical tools to simulate diffusion processes (pollutant, water...) moving in heterogenous media in the presence of interfaces.
- Earthquake forecasting is notoriously difficult. To grasp the statistical distribution of seismic hazards, we consider setting up tools to detect seismic faults using marked point processes. Such a project presents challenging aspects concerning both the inference and the simulation of the processes.
On such topics, we hold long standing interdisciplinary collaborations with INRAE Grenoble, the RING Team (GeoRessources, Université de Lorraine), IMAR (Institute of Mathematics of the Romanian Academy) in Bucharest.
4.2 Astronomy
We have longstanding and continuous cooperation with astronomers and cosmologists in France, Spain and Estonia. In particular, we are interested in using spatial statistics tools to detect galaxies and other star patterns such as filaments detection. Such developments require us to design specific point processes giving appropriate morpho-statistical distributions, as well as specific inference algorithms which are based on Monte Carlo simulations and able to handle the large volume of data.
4.3 Complex systems for healthcare, insurance, social networks and telecommunication networks
Graphs are essential to model complex systems such as the relations between agents, the spatial distribution of points that are connected such as stars, the connections in telecommunication networks, and so on. We develop various directions of the study of random graphs that are motivated by a large class of applications:
- The success of organ transplant operations depends on their capacity to comply in real time, with sharp compatibility constraints. Here, vertices represent at any given time receivers and donors, while edges represent compatibilities. To improve the quality of such life-saving medical acts, we work on the optimization and control of organ transplant systems by stochastic matching models, namely, queueing models in which elements are matched in real time, following prescribed compatibility constraints.
- The modeling of epidemics, viruses on computer networks and message percolation on large social networks can be addressed using the theory of large graph asymptotic on random graphs. In particular, we work on Markov exploration algorithms on large Configuration Model graphs, to propose weak, but tractable approximations of such propagation phenomena on large networks.
- We have longstanding collaborations in the domain of performance analysis of telecommunication networks. In particular, we worked on the modeling and analysis of queuing systems with reneging with applications to real-time networking; on the performance analysis of parallel service systems, and the large-network analysis of CDMA-type (Code Division Multiple Access) communication protocols, using random graph modeling. We also considered ad-hoc networking and the Internet of Things (IoT). Using graph and game theory techniques, we aim at a proper definition, and dynamical analysis, of the notion of trust between agents of these networks.
- Using random field models on graphs, we have considered the simulation and inference of the relations between bibliographical data related to scientific literature. This provides us with an application of our techniques in the field of dynamical evolution of networks.
- We study the spatial distribution of random -tessellation with the aim of providing models for agricultural parcels. Again, such a problem presents challenging aspects both for simulation and inference.
- Finally, we consider personalized recommendation systems for insurance which are based on life events, using self-excited processes. We developped techniques based on Hawkes processes and improve the existing approaches.
We have longstanding collaborations on these topics with Agence de Biomédecine (ABM), Le Foyer (insurance company, Luxembourg), INRAE (Avignon), Lip 6, UTC, LORIA (computer science laboratory, Nancy), University of Buenos Aires, Northwestern University and LAAS (CNRS, Toulouse).
4.4 Digital Humanities
Digital Humanities represents an interdisciplinary field of research. We are interested in developing suitable, automatic tools to help experts to study the ideas contained in antique texts. Together with historians of antiquity, we considered one of the founding texts of political sciences, the Politics of Aristotle. To fulfill our purposes, we consider techniques from the history of antiquity, machine learning, and statistics. This presents some technological challenges to develop suitable tools to load and manipulate the data.
This research was supported by the Inria Exploratory Reasearch Action Apollon (2022-2024) and by CNRS. It involves collaboration with researchers from Archimède (Universities of Strasbourg and Haute-Alsace), IRIMAS and CRESAT (Université de Haute-Alsace) and University of Pavia.
5 Highlights of the year
Radu Stoica published a book Random Patterns and Structures in Spatial Data (Chapman and Hall) 25 that proposes a general mathematical framework for detecting and characterising, from a morphological and statistical point of view, the hidden structures in spatial data.
6 Latest software developments, platforms, open data
6.1 New platforms
Participants: Antoine Lejay, Radu Stoica, Saïd Toubra.
DRLIB is a C++ library built for performing modeling, simulation and statistical inference based on marked point processes with interaction. This library is the result of a joint project of Radu Stoica with Didier Gemmerlé (CNRS research engineer at IECL).
Palamède aims at being a collaborative plateform to vizualize, annotate and analyze texts from the point of view of experts in history, philology or more generally in social sciences. The short term goals are to incorporate tools from Artifical Intelligence to ease the study of texts. This plateform is supported by the ADT (Action de développement Technologique) Apollon.
7 New results
7.1 Analysis and simulation of Stochastic Differential Equations: thresholds and singularities
Participants: Julia Budzinski, Madalina Deaconu, Antoine Lejay, Sara Mazzonetto.
The numerical approximation of Stochastic Differential Equations (SDEs) and in particular new methodologies to approximate hitting times of SDEs is a challenging problem which is important for a large class of practical issues such as: geophysics, finance, insurance, biology, etc.
With Samuel Herrmann (Université de Bourgogne), Madalina Deaconu achieved significant progress on this topic by developing new methods that are both simple to implement and efficient. We pursued this topic by developping the approximation of diffusion exit times from bounded domains using a rejection-based random walk on truncated spheroids. The proposed approach relies on an acceptance–rejection procedure applied to random walk trajectories. These trajectories, modeled as random walks on spheroids that approximate the paths of Brownian motion, were originally introduced to solve the Brownian exit problem in -dimensional space. In this approach, we introduce a substantial modification by replacing spheroids with truncated spheroids, which enables the extension of results obtained for Brownian paths to more general diffusion processes.
Madalina Deaconu , together with Samuel Herrmann (Université de Bourgogne) and Cristina Zucca (University of Torino), continued their work on the exact simulation of the hitting times of multi-dimensional diffusions.
Existence and uniqueness results for one-dimensional stochastic processes solution to SDEs, are important because lack of uniqueness may affect approximation or inference results. In an ongoing work, Sara Mazzonetto , Alexis Anagnostakis (IECL Metz) and Pierre Etoré (LJK Grenoble) are dealing with different questions about the non-uniqueness of solutions for processes solution to SDEs with a diffusion coefficient admitting jumps and becoming negative. We tackle a conjecture that has been open since the 80's. We have obtained a partial answer and we are seeking for the link with sticky-skew diffusions. In the last year we obtained an alternative proof. We are exploring different approaches to extend the class of coefficients we can deal with.
On another ongoing work with Benoît Nieto (former postdoc at École Polytechnique, now working at ESILV), Sara Mazzonetto is considering theoretical results on existence and uniqueness of solutions to SDEs with singularities: degenerating diffusion coefficient, distributional drifts, or discontinuous coefficients. We apply these results to prove strong existence and uniqueness for solution to several-regimes CIR (Cox-Ingersoll-Ross) which presents both degenerate diffusion and discontinuous coefficients. The inference for this model has already given rise to a publication 15.
Julia Budzinski , under the supervision of Madalina Deaconu and Sara Mazzonetto , is considering a probabilistic numerical approximation scheme for SDEs with singular coefficients. Althought some convergence results exist for the Symetrized Euler scheme applied to CIR with continuous coefficients and for the Euler scheme applied to SDE with discontinuous coefficients, no such convergence results are available for the Symetrized Euler scheme applied to CIR with discontinuous coefficients.
Madalina Deaconu , Lucian Beznea (IMAR, Bucharest) and Oana Lupaşcu-Stamate (Gheorghe Mihoc–Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Bucharest) are developing a stochastic approach for the two-dimensional Navier-Stokes equation in a bounded domain. More precisely we consider the vorticity equation and construct a specific non-local branching process. This approach is new and may conduct to important advances as it will also results in a new numerical algorithm if successful.
In particular, we obtained several results concerning the construction of a duality - time reversal process and also in the development of a numerical algorithm with a non-local branching process involving the creation and disappearance of particles that mimic the physics of the vorticity in the boundary layer.
7.2 Stochastic dynamics with jumps
Participants: Madalina Deaconu, Antoine Lejay.
We have a strong interest in the fragmentation equation for understanding snow or rock avalanches. Our point of view is to explore the probabilistic representations of transport equations in this framework as well as the possibilities they offer.
Madalina Deaconu and Antoine Lejay , together with Gaetano Agazzotti (former intern in the team), have studied in 12 the evolution of the moments of a self-similar fragmentation equation from an analytic viewpoint. In particular, we have shown existence for an initial condition which is a measure. We have proved rigorously its asymptotic behavior.
Madalina Deaconu , together with Oana Lupaşcu-Stamate (Gheorghe Mihoc–Caius Iacob Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy), studied the asymptotic behaviour of an avalanche model through a discret non-conservative binary coagulation-fragmentation equation 13. The model develops self-organized critical systems and in particular a simple sand pile model. This approach furnishes a new interpretation of the avalanche phenomena by handling stochastic differential equations with jumps. The model is completed by numerical simulations.
7.3 Inference of singular or regular Stochastic Differential Equations
Participants: Julia Budzinski, Antoine Lejay, Sara Mazzonetto.
Antoine Lejay and Sara Mazzonetto continued to improve their work on an expansion of the maximum likelihood estimator using formal series expansions 31 with a view toward stochastic differential equations with singular coefficients. The aim of this work is to understand the lack of Gaussianity in the non-asymptotic regime.
Sara Mazzonetto and Benoit Nieto (ESILV), consider several-regimes CKLS (Chan-Karolyi–Longstaff– Sanders) dynamics (including Cox-Ingersoll-Ross model) and studied parameter estimation from high-frequency observations. This result allows to consider new dynamics and recover the previously treated dynamics. During this year, improvement of the results have been provided leading to a publication 15.
With Paolo Pigato (University Tor Vergata, Roma), Sara Mazzonetto worked on new estimators from low frequency observations for the parameters of several regimes threshold models which show mean-reversions features 37. They consider also non-stationary regimes.
Julia Budzinski is working on using these results, among others such as 36, for modeling Realized Volatility data. The objective is to perform a comparative analysis of exponential Ornstein-Uhlenbeck and CIR models with and without threshold using both simulated and real Realized Volatility datasets. To this end, she is developing algorithms to jointly estimate drift, volatility and thresholds and then test the presence of one or more thresholds in the drift. One of the statistical tests for thresholds detection is based on Monte Carlo methods which require the ability to simulate the underlying process. The Euler scheme is used for the Ornstein-Uhlenbeck while the symmetrized Euler scheme is used for the CIR. Comparison of the models is based on statistical criteria that penalized the model complexity such as the Akaike Information Criterion (AIC).
Sara Mazzonetto and Alexis Anagnostakis (postdoc at IECL Metz) have been extending their respective results on high-frequency approximation of the local time of sticky-oscillating-skew diffusion processes. Via some new functional limit theorems for sticky diffusions, they estimate the parameters of stickiness and/or skewness 27. The main goal is to reach rates of convergence for sticky diffusions and so extend the results in the publication 16. We improved a partial interesting result for sticky Brownian motion presented in 34.
7.4 Hawkes processes for plant deases
Participants: Madalina Deaconu.
Hawkes point processes model phenomena in which the occurrence of an event triggers the arrival of other events of the same type. With Katarzyna Adamczyk (INRAE), Madalina Deaconu proposed a modeling based on this process in order to study apple scab, a disease of apple trees caused by the pathogenic fungus Venturia inaequalis 22. The Hawkes model proposed for the emission of fungal spores takes into account meteorological covariates that may trigger this emission. The results show that the estimator of the conditional intensity of the process can be considered as a relevant indicator of the risk of contamination of apple trees.
Work is in progress on this topic as we are developping Hawkes process with time-varying baseline intensity influenced by dynamic covariates. The main objective of the project is to study the asymptotic properties of estimators in this model. We will work in a Bayesian framework, aiming for posterior contraction and, if possible, selection consistency under sparsity-inducing priors, while benefiting from natural uncertainty quantification.
7.5 Application of Approximate Bayesian Computation algorithms for parameter estimation for Gibbs point processes based on partly missing data
Participants: Nathan Gillot, Radu Stoica.
In galactic patterns, some of the data is often missing and methods to characterise such patterns need to be developed. We focus on Gibbs point processes in a bounded region , observable only in . In this situation, the likelihood of the underlying point process cannot be derived from the available observations, unless simulated data is produced via Markov Chain Monte Carlo (MCMC) procedures in the region , where direct observations are not available. This operation increases the general computational cost and the convexity of the likelihood can not be guaranteed. In order to overcome this drawback, Radu Stoica , Nathan Gillot , Didier Gemmerlé (IECL, Université de Lorraine) and Aila Särkkä (Chalmers University, Sweden) used an Approximate Bayesian Computation (ABC) framework to estimate the model parameters based on partly missing data. This framework allows a theoretical construction of Metropolis-Hastings dynamics that samples from the joint distribution of the unobserved pattern and the parameter of interest, conditionally on the observed data. The theoretical properties of the proposed dynamics enable the construction of different approximate algorithms that exhibit good convergence properties. The proposed method is applied to simulated and real data 23.
7.6 Modeling in geophysics: fault observations and inference
Participants: Radu Stoica.
Radu Stoica with Guillaume Caumon, Fabrice Taty-Moukati and François Bonneau (all at GeoRessources, Université de Lorraine) integrated human interpretation to downscale machine learning-based fault likelihood images into potential fault networks using the Candy Model, a marked point process that simulates networks consistently with input images 21. Parameters are inferred from expert networks using the ABC Shadow algorithm. Applied to three fault interpretations, the method successfully generates alternatives, though better control of branching and relay zones is needed. The workflow bridges computational uncertainty quantification and human-based approaches for subsurface forecasts.
With Amandine Fratani, Guillaume Caumon, Jeremie Giraud, Romain Baville, Chiara-Luna Prest, Christophe Antoine (GeoRessources, Université de Lorraine), we are interested in using expert rules to model fault networks from incomplete data using graph formalism, where nodes represent fault observations and edges indicate potential associations. This approach, previously applied to 2D seismic images, is adapted here for borehole data. Three new expert rules incorporate borehole-specific information: orientation (dip and dip direction), position, and aperture. A new sampling algorithm efficiently manages large drilling campaigns in mining, producing fault scenarios consistent with these rules.
Finally, with Amandine Fratani, Guillaume Caumon, Jeremie Giraud (GeoRessources, Université de Lorraine) and Vitaliy Ogarko, Mark Jessel, Guillaume Pirot (Centre for Exploration Targeting, University of Western Australia), we consider the creation of a synthetic training database for fault observations association. Geological models in sedimentary basins are constrained by interpreting faults and horizons in seismic and drillhole data. Data sparsity allows multiple fault networks from a single observation set. Graph formalism with nodes representing observations and edges carrying association potentials addresses this. Machine learning, specifically Random Forest, can compute these potentials, but limited open-access structural models restrict its application. This work develops a synthetic structural model database featuring normal faults using modified Noddy code. Faults are grouped into families with similar orientations defined by mean dip and dip direction. Individual fault orientations are sampled from a Kent distribution. Resulting models are smoothed in geological software, then sampled to train a Random Forest for retrieving association potentials.
7.7 Exploration algorithms of large random graphs
Participants: Pascal Moyal.
We have pursued our research activity on the Markovian analysis of various Markovian exploration algorithms on random graphs, analyzed and/or approximated to the large graph limits, using scaling limits of stochastic processes, on three distinct classes of random graphs: Configuration models, Stochastic block models, and Preferential attachment models.
In a revision of 30, with Vincent Robin and Mohamed Habib Dialo Aoudi (UTC), we enriched our theoretical results with a tractable numerical scheme for the competitive ratio of online matching algorithms on large graphs. Using hydrodynamic limits for the Configuration model, matching coverage is computed by solving ODEs. We aim at extending this to exploration algorithms such as breadth-first search and coloring on random graphs.
For multiclass online Stochastic block models, 17 gives necessary and sufficient conditions for the existence of a perfect matching infinitely often, and moment bounds for the number of unmatched nodes, by Lyapunov techniques.
With Mariana Olvera-Cravioto (University of North Carolina), we are investigating the connected out-component of vertices in large oriented preferential attachment graphs (Barabasí-Albert model). Using Markov in-depth exploration and coupling methods, we show that the local limits follow a multi-type Galton-Watson process. This has crucial implications for the asymptotic analysis of preferential attachment models in epidemiological and social media applications.
7.8 Optimization of queueing systems: Reinforcement learning and Markov control
Participants: Pascal Moyal.
Pascal Moyal has dedicated an important part of his research activity on two ongoing projects on the stochastic optimization and control of queueing systems.
First, with Céline Comte (LAAS-CNRS), we generalized quasi-reversibility for Continuous-time Markov chains (CTMC's), enabling simple quasi-product form representations of stationary distributions, a crucial feature for long-run simulation and equilibrium analysis. This general quasi-reversibility property holds in particular for a large class of queueing systems among which, Whittle networks and Order-Independent (OI) queues. When complemented with a balanced access control mechanism, the quasi-reversibility property of the system is conserved and a simple quasi-product form holds for the stationary distribution 29. Besides, this allows to implement simple and efficient algorithms to optimize the access control in function of the system state. Finally, as observed in a few cases in 29, reinforcement learning algorithms of the Policy gradient (RLPG) type appear to be particularly efficient in this context. We are currently working at an extensive analytical study of the performance of these algorithms in a much broader range of systems.
In a second line of work, Pascal Moyal and Thomas Masanet (former PhD student, now teacher) worked in collaboration with Christian Jacquelinet and Benoît Audry (Agence de la Biomédecine - ABM) at the optimization of organ transplant networks. They proposed in 14 an allocation policy based on Earliest Simulated Deadline First (ESDF) queueing. Extensive simulations show ESDF performs better than the current Score algorithm (implemented by the ABM at the nationwide scale) in equity across indication classes for liver transplants, especially during organ shortage, while maintaining comparable death rates. These results are promising since ESDF is easier to implement and explain to patients, yet performs better. Current work focuses on providing analytical proofs of ESDF optimality and extending the study to cross-kidney transplants with compatibility constraints on general graphs. This leads to a control problem of dynamic matching models.
7.9 Comparing critical editions of ancient texts
Participants: Antoine Lejay, Lionel Lenotre.
Within the Némésis grant from MITI CNRS, we have developed a methodology to compare variants between two critical editions of the same text. The core methodology relies on an ad hoc format to store a text as a sequence of tokens embedding metadata. To overcome the limitations of the XML-TEI encoding, which is classically used for ancient texts, a representation with hypergraphs supersedes a tree based representation in order to account for the overlapping division of the text. The differences were automatically classified. The method was applied to two high-quality digitized versions of critical editions of Aristotle's Politics.
7.10 Geometric features of nested regressions and loss landscape
Participants: Antoine Lejay, Lionel Lenotre, Saïd Toubra.
We are studying the effect of nested regression in linear least-squares on the geometry of the loss landscape. Considering the product of two matrices in a linear least-squares regression instead of a single matrix leads to a radically different structure of the loss landscape, with the introduction of many saddle points, as pointed out by Baldi and Hornik in 35. Using tools from geometry and optimization, we aim at providing a better description of the loss landscape and its impact on gradient descent algorithms. This work is motivated by the fact that up to a non-linear transformation, the attention mechanism, which is central in the transformers' architecture, actually performs a nested regression. This work then aims at being applied to provide a better understanding of the mechanisms of Large Language Models (LLM) and related neural networks.
8 Partnerships and cooperations
8.1 International initiatives
8.1.1 STIC/MATH/CLIMAT AmSud projects
Projet Math AmSud EXPLORE-SDE
Participants: Antoine Lejay.
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Title:
Explosions for non-Markovian and related stochastic differential equations
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Partner Institutions:
- Inria, France
- Universidad de Valparaíso, Chile
- Universidad Adolfo Ibañez, Chile
- Universidad de Chile, Chile
- Universidad de la República, Uruguay
- Universidad Nacional de Colombia
- Université Côte d’Azur, France
- Université Paris Saclay, France
- Université de Lille
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Date/Duration:
January 2025-December 2026
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Additionnal info/keywords:
The PIs are Étienne Tanré and Soledad Torres.
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Summary:
The project aims at studying the explosions phenomena for non-Markovian and related stochastic differential equations, such as fractional Brownian motion.
8.1.2 Participation in other International Programs
Projet ECOS SUD-CHILI C23E06
Participants: Sara Mazzonetto.
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Title:
Constrained Stochastic Differential Inclusions involving Normal Cones
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Partner Institutions:
- Lorraine University, France
- Universidad de O’Higgins, Chile
- Universidad Técnica Federico Santa María, Chile
- Burgundy University, France
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Date/Duration:
January 2024-December 2026
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Additionnal info/keywords:
The PIs are Nabil Kazi-Tani (IECL, Metz) and Emilio Vilchez (O'Higgins University, Rancagua).
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Summary:
The project aims to study random and stochastic versions of sweeping processes. In some cases, theses processes can be seen as a generalization of reflected stochastic processes evolving into moving sets. Sara Mazzonetto works on defining specific stochastic sweeping processes and related set estimation questions.
8.2 International research visitors
8.2.1 Visits of international scientists
Other international visits to the team
Randolf Altmeyer
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Status
associate professor
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Institution of origin:
Imperial College London
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Country:
UK
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Dates:
13-14/11/2025
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Context of the visit:
Seminar in the Probability and Statistics team of IECL and collaboration with Sara Mazzonetto
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Mobility program/type of mobility:
research stay
Ed Cohen
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Status
associate professor
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Institution of origin:
Imperial College London
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Country:
United Kingdom
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Dates:
22-25/04/2025
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Context of the visit:
Collaboration with Radu Stoica
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Mobility program/type of mobility:
research stay - EXCOSM project
El Mehdi Haress
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Status
post-doctoral fellow
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Institution of origin:
University of Leeds, School of mathematics
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Country:
United Kingdom
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Dates:
23-26/11/2025
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Context of the visit:
collaboration with the team and participation to the PASTA Meeting Conference 24-25 November 2025
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Mobility program/type of mobility:
research stay
Aila Särkkä
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Status
full professor
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Institution of origin:
Chalmers University
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Country:
Sweden
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Dates:
13-16/10/2025
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Context of the visit:
collaboration with Radu Stoica, Nathan Gillot and Didier Gemmerlé
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Mobility program/type of mobility:
research stay - EXCOSM project
Giorgos Vasdekis
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Status
Lecturer
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Institution of origin:
Newcastle University
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Country:
UK
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Dates:
4-7/11/2025
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Context of the visit:
Collaboration with Sara Mazzonetto
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Mobility program/type of mobility:
Visit to the Probability and Statistics Team of IECL.
8.2.2 Visits to international teams
Research stays abroad
Julia Budzinski
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Visited institution:
Rome Tor Vergata University
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Country:
Italy
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Dates:
6/10/2025-16/12/2025
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Context of the visit:
collaboration with Paolo Pigato in a Dream Mobility Grant, founded by Université de Lorraine
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Mobility program/type of mobility:
research stay
Madalina Deaconu
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Visited institution:
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest
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Country:
Romania
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Dates:
8/09/2025-15/09/2025
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Context of the visit:
collaboration with Lucian Beznea and Oana-Lupaşcu Stamate
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Mobility program/type of mobility:
research stay
Madalina Deaconu
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Visited institution:
University of Torino
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Country:
Italy
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Dates:
8/06/2025-11/06/2025
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Context of the visit:
Seminar and collaboration with Cristina Zucca
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Mobility program/type of mobility:
research stay
Sara Mazzonetto
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Visited institution:
University of Turin
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Country:
Italy
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Dates:
18/05/2025-24/05/2025
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Context of the visit:
Seminar and collaboration with Bruno Toaldo
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Mobility program/type of mobility:
research stay
Sara Mazzonetto
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Visited institution:
Rome Tor Vergata University
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Country:
Italy
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Dates:
27/10/2025-31/10/2025
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Context of the visit:
collaboration with Paolo Pigato
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Mobility program/type of mobility:
research stay
Sara Mazzonetto
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Visited institution:
Center for Mathematical Modeling and O'Higgins University
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Country:
Chile
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Dates:
06/12/25-11/12/25
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Context of the visit:
Ecos SUD Project.
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Mobility program/type of mobility:
research stay
8.3 European initiatives
Participants: Nathan Gillot, Freja Nørby, Radu Stoica.
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Title:
HORIZON WIDERA TWINNING EU Project : EXCOSM - Building excellence in the study of galaxies and cosmology at University of Tartu
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Partner Institutions:
- Université de Lorraine
- Tartu University (Estonia)
- Leibniz institute for Astrophysics Potsdam (Germany)
- University of Groningen (Germany)
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Date/Duration:
Octorber 2024-September 2027
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Additionnal info/keywords:
Radu Stoica is the PI for Université de Lorraine.
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Summary:
The EXCOSM project enhances galaxy evolution research by combining observational data, simulations, and cosmic web theory to understand how galactic environments influence star formation and mass assembly. Through international collaboration, the University of Tartu will develop advanced methods for modeling the cosmic web, strengthening its research capacity and global visibility in these fundamental cosmological studies.
8.4 National initiatives
Participants: Antoine Lejay, Lionel Lenotre, Saïd Toubra.
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Title:
Nouvelles Études en Humanités Numériques (Némésis)
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Partner Institutions:
- Inria, France
- Université de Haute-Alsace
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Date/Duration:
January 2024-December 2025
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Additionnal info/keywords:
The PIs are Maria-Teresa Schettino and Antoine Lejay.
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Summary:
This grant (funding: programme Blanc MITI CNRS) supports the interdisciplinary research in the field of Digital Humanities, namely the development of the Palamède software within the Apollon project and the PhD thesis of Saïd Toubra .
8.5 Public policy support
Participants: Antoine Lejay.
- Antoine Lejay worked in a contract with Polyor SAS on the prediction of nitrite in agricultural use, with a grant from the Métropole du Grand Nancy.
9 Dissemination
9.1 Promoting scientific activities
9.1.1 Scientific events: organisation
- Madalina Deaconu organized the PASTA Seminar and Working Group, the PASTA Day in June and the PASTA Meeting in November.
- Antoine Lejay organized a joint workshop Pôle AM2I Chambre d'Agriculture in June and a workshop Mise en place de l'IA as an Atelier du Pôle AM2I in November, both at Université de Lorraine.
- Sara Mazzonetto co-organized the annual one day Colloquinte of the Probability and Statistics team of Institut Élie Cartan de Lorraine, in June.
- Sara Mazzonetto and Pascal Moyal co-organized a workshop of two days First IECL Probability and statistics days, Interaction with MaGE federation and Grand Region in Nancy in November.
- Pascal Moyal organized the mini-symposium Optimization of Stochastic and dynamic matching systems at the Informs Applied Probability Society Conference in Atlanta (USA) in July.
- Radu Stoica was member of the scientific organising committee of the EXCOSM Summer School Large scale structure of the Universe: from galaxies to cosmology in Haapsalu (Estonia) in July.
Member of the conference program committees
- Madalina Deaconu is member of the Coordinating Committee of the French-Romanian Colloquium on Applied Mathematics (4 members: 2 in France and 2 in Romania), she is the expert in the Probabilities and Statistics area on the French side. This conference has been held every two years for the past 30 years.
- Antoine Lejay was member of the scientific committee of Journées de Probabilités 2025, in Marseille in June.
9.1.2 Journal
Member of the editorial boards
- Antoine Lejay is co-editor of Séminaire de Probabilités, and associate editor of Mathematics and Computers in Simulation.
- Pascal Moyal is associate editor of Queueing Systems - Theory and applications.
- Radu Stoica is associate editor of Annals of the Institute of Statistical Mathematics, and member of the editorial board of Spatial Statistics.
Reviewer - reviewing activities
- Madalina Deaconu wrote reviews for: Quantitative Finance.
- Antoine Lejay wrote reviews for: Annales de la Faculté des Sciences de Toulouse, Electronic Journal of Probability, IMA Journal of Numerical Analysis, Journal of Evolution Equations, Journal of Mathematics, Journal of Computational Physics, Mathematics and Computers in Simulation, and Physical Review E.
- Sara Mazzonetto wrote reviews for Annals of Applied Mathematics, Journal of Mathematical Analysis and Applications, and Journal of Statistical Physics.
- Pascal Moyal wrote reviews for Queueing Systems: Theory and Applications, The Annals of Applied Probability, and Computer Networks.
- Radu Stoica wrote reviews for Spatial Statistics and Annals of the Institute of Statistical Mathematics.
9.1.3 Invited talks
- Madalina Deaconu gave an invited talk to the conference Through the threshold: first passage times and beyond, Celebrating the career of Laura Sacerdote in Torino (Italy) in June. She gave also an invited talk in the 12th International Conference on Stochastic Analysis and its Applications (ICSAA 2025) in Bucharest (Romania) in September.
- Antoine Lejay gave a mini-course at the 10th Regional Summer School on Applied Mathematics in Sinaia (Romania) in July.
- Sara Mazzonetto gave three invited conference talks and four invited online or in presence seminars. Invited conference talks in the Probability session of SMF conference in Dijon in June, FNRS Contact Group in October in Liège (Belgium), in the Fourth Workshop on Stochastic Analysis and Optimization, applied to economics, finance, energy and insurance in Peurto Natales (Chile) in December. Online PRISMA seminar in June, and in presence seminars in Versailles in March, Turin in May, Lille in July.
- Pascal Moyal was a plenary speaker at the workshop Product Form Probability Distributions in Eindhoven (Netherlands) in May.
- Radu Stoica gave a seminar at CWI (Amsterdam, The Netherlands) in March. He gave a course at the EXCOSM summer school Large scale structure of the Universe in Haapsalu (Estonia) in July. He was also invited to give talks at the Mathematical Foundations of AI (a Workshop organised by DATAIA Institute and SCAI) in Paris in March and at the Joint Statistical Meeting in Nathville (USA) in August.
9.1.4 Scientific expertise
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Madalina Deaconu is Deputy Head of Science of Inria Centre at Université de Lorraine and Inria branch at Université de Strasbourg since January 2022.
She is also, at the national level, member of the Evaluation Commission of Inria. In this context she was:
- Member of the Promotion Inria Committee.
- Member of the Individual “primes” Committee.
She is also member of Bureau du Comité de Projets and Comité des Projets of Inria Centre at Université de Lorraine.
Madalina Deaconu was
- Member of the Inria Admissibility National Committee for Senior Researchers (Second Class Research Directors - DR2).
- Member of the Committee of hiring young researchers (CRCN and ISFP) at Inria Saclay Centre.
She was member of the PhD hiring committee of IECL.
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Antoine Lejay is a member of the board the AMIES.
He is also the Vice-Director of the Pôle AM2I in charge of scientific animation. The Pôle AM2I gathers 6 laboratories of Université de Lorraine related to mathematics, computer sciences and automatic control (CRAN, IECL, LCFC, LCOMS, LGIPM, LORIA) with the goal of fostering interdisciplinary projects.
He is also co-head of the COMIPERS, which is the local hiring committee for PhD and post-doctoral students at Centre Inria de l'Université de Lorraine.
He was Member of a hiring committee for an Assistant Professor position at Institut Élie Cartan de Lorraine, Metz.
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Sara Mazzonetto is elected member of the IECL Laboratory Council since 2024.
She is member of the PhD hiring committee of IECL since 2024.
She is one of the organiser of an internal seminar of the Probability and Statistics group at IECL since September 2022.
She was a member of a hiring commitee for an Assistant Professor position at Institut Élie Cartan de Lorraine, Nancy.
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Pascal Moyal is Head of the Probability ans Statistics team (36 faculty members) at IECL. As such, he is also:
- Member of the Executive committee of IECL;
- Invited Member of the IECL Laboratory council;
- Member of the PhD hiring committee of IECL.
He is member of the Internal committee (commission du personnel) of IECL.
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Radu Stoica is member of the International Strategy Think Tank of the Université de Lorraine.
He is in charge of the international relations of the IECL Laboratory.
9.2 Teaching - Supervision - Juries - Educational and pedagogical outreach
Pascal Moyal and Radu Stoica are professors. They have full teaching duties with lectures at all the levels of the university. Sara Mazzonetto is assistant professor, who was on partial leave this year. For them all, we mention here only lectures at Master 1 and Master 2 levels as well as responsibilities.
- Madalina Deaconu , Stochastic Modeling, 30h, M2, Master IMSD, Université de Lorraine.
- Madalina Deaconu , Monte Carlo Simulation, 24h, M1, Financial Mathematical Engineering, Université de Lorraine.
- Madalina Deaconu , Random Variable simulation, 12h, M1, École des Mines de Nancy, Université de Lorraine.
- Antoine Lejay , Simulation des marchés financiers, 23h, M2, Master PSA, Université de Lorraine.
- Antoine Lejay , Financial mathematics, 18h, M2, Master IMSD, Université de Lorraine.
- Sara Mazzonetto , Probability and Statistics, 25h, M1, Master IMSD and MFA, Université de Lorraine.
- Sara Mazzonetto , Stochastic calculus for finance, 16h, M2, Master IMSD, Université de Lorraine.
- Pascal Moyal is Head of the Working Group Master IA of Université de Lorraine.
- Pascal Moyal , Financial mathematics, 25h, M2, Master IMSD, Université de Lorraine.
- Pascal Moyal , Stochastic calculus for finance, 9h, M2, Master IMSD, Université de Lorraine.
- Pascal Moyal , Reinforcement learning, 12h, M2, Master IMSD, Université de Lorraine.
- Pascal Moyal , Stochastic modeling, 12h, M2, Master IMSD, Université de Lorraine.
- Pascal Moyal , Random graphs and their applications, 30h, M2, Master MFA, Université de Lorraine.
- Pascal Moyal , Graph theory and Neural networks, 30h, M1, Master Math., Université de Lorraine.
- Pascal Moyal , Stochastic calculus, 24h, Master level, Telecom Paristech.
- Pascal Moyal , Stochastic networks, 17h30, Master level, Mastère Parisien de Recherche Opérationnelle, CNAM.
- Pascal Moyal , Operations research, Master level, Mastère TET, École des Ponts et Chaussées.
- Radu Stoica is the head of the Master M2 IMSD Ingénierie Mathématique et Science des Données, Université de Lorraine.
- Radu Stoica , Simulation and Inference via Monte Carlo Methods, 28h, M1, Master IMSD, Université de Lorraine.
- Radu Stoica , Spatial Statistics and Bayesian Inference, 36h, M2, Master IMSD, Université de Lorraine.
9.2.1 Supervision
- PhD in progress, Lorenzo Agabiti , High-order expansions in rough paths analysis, Sorbonne Université, since October 2024, funding COFUND FSMP, supervised by Antoine Lejay and Lorenzo Zambotti (Sorbonne Université, Paris).
- PhD in progress: Julia Budzinski , Simulation of diffusions with discontinuous coefficients, Université de Lorraine, since November 2023, funding Inria, supervised by Madalina Deaconu and Sara Mazzonetto .
- PhD in progress: Amandine Fratani, Interpretation of seismic faults by graph-based machine learning, Université de Lorraine, since November 2022, funding RING consortium, supervisded by Guillaume Caumon (Georessources, Université de Lorraine) and Radu Stoica .
- PhD defended in December 2025: Nathan Gillot , Models and algorithms for statistical learning of marked space-time point processes. Application: analysis and characterization of cosmological data, Université de Lorraine, since November 2022, funding CNRS, supervised by Radu Stoica .
- PhD in progress: Freja Nørby, Walls and voids in the spatial distribution of galaxies: morphology, hierarchical topology and statistical characterisation of the cosmic web, University of Tartu, University of Groningen, since September 2025, funding: EXCOSM project and University of Tartu, supervised by Radu Stoica , E. Tempel and R. van de Wejgaert.
- PhD in progress: Saïd Toubra , Geometric Interpretation of Embeddings in Neural Networks, Université de Lorraine, since October 2024, funding CNRS, supervised by Antoine Lejay and Lionel Lenotre (IRIMAS, Université de Haute-Alsace).
9.2.2 Juries
- Madalina Deaconu : Examinator for the HDR of Boris Arcen, Université de Lorraine, May.
- Madalina Deaconu : Examinator for the PhD of Anouk Rago, Université de Lorraine, June.
- Antoine Lejay : Examinator for the PhD of Paul Maurer, Université-Nice Côte d'Azur, November.
- Antoine Lejay : Examinator for the PhD of Mathis Fitoussi, Université Paris-Saclay, December.
- Radu Stoica : Examinator for the PhD of Zhuldzay Baki, University of Twente (The Netherlands), December.
9.3 Popularization
9.3.1 Participation in Live events
- Sara Mazzonetto was an Ambassador for the first edition of the day Sciences, un métier de Femmes in Nancy in February.
- Sara Mazzonetto was a témoin for an online speed meeting session organized by Femmes et Mathematiques in April.
9.3.2 Others science outreach relevant activities
- Antoine Lejay is editor in chief of the Success stories (2 pages presentation of a successful industrial collaboration, Agence Mathématiques en Entreprises et Interactions (AMIES) and Fondation Sciences Mathématiques de Paris).
10 Scientific production
10.1 Major publications
- 1 articleStochastic equation of fragmentation and branching processes related to avalanches.Journal of Statistical Physics1624February 2016, 824-841HALDOI
- 2 articleInitial-boundary value problem for the heat equation - A stochastic algorithm.Annals of Applied Probability2832018, 1943-1976HALDOI
- 3 articleProbabilistic representations of fragmentation equations.Probability Surveys202023, 226-290HALDOI
- 4 articleConstructing general rough differential equations through flow approximations.Electronic Journal of Probability272021, 1-24HALDOI
- 5 articleMaximum likelihood estimator for skew Brownian motion: the convergence rate.Scandinavian Journal of StatisticsFebruary 2023HALDOI
- 6 articleParameters estimation of a Threshold CKLS process from continuous and discrete observations.Scandinavian Journal of Statistics5242025, 1670-1707HALDOI
- 7 miscRates of convergence to the local time of Oscillating and Skew Brownian Motions.October 2021HAL
- 8 articleA product form for the general stochastic matching model.Journal of Applied Probability582June 2021, 449-468HALDOI
- 9 articleA stochastic matching model on hypergraphs.Advances in Applied Probability5342021, 951-980HALDOI
- 10 inproceedingsBayesian statistical analysis of hydrogeochemical data using point processes: a new tool for source detection in multicomponent fluid mixtures.RING Meeting 2020Nancy, FranceSeptember 2020HAL
- 11 articleShadow Simulated Annealing: A new algorithm for approximate Bayesian inference of Gibbs point processes.Spatial StatisticsApril 2021HALDOI
10.2 Publications of the year
International journals
International peer-reviewed conferences
Conferences without proceedings
Scientific books
Doctoral dissertations and habilitation theses
Reports & preprints
Other scientific publications
10.3 Cited publications
- 34 unpublishedOn the number of crossings and bouncings of a diffusion at a sticky threshold.October 2024, working paper or preprintHALback to text
- 35 articleNeural networks and principal component analysis: Learning from examples without local minima.Neural Networks21January 1989, 53–58URL: http://dx.doi.org/10.1016/0893-6080(89)90014-2DOIback to text
- 36 articleDrift estimation of the threshold Ornstein-Uhlenbeck process from continuous and discrete observations.Statistica Sinica3412024, 313-336HALDOIback to text
- 37 unpublishedEstimation of parameters and local times in a discretely observed threshold diffusion model.March 2024, working paper or preprintHALback to text