Bibliography

Major publications by the team in recent years

• 1P. Balança.
  A increment type set-indexed Markov property, 2012.
  http://arxiv.org/abs/1207.6568
• 2J. Barral, J. Lévy Véhel.
  Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments, in: Electronic Journal of Probability, 2004, vol. 9, pp. 508–543.
• 3O. Barrière, J. Lévy Véhel.
  Application of the Self Regulating Multifractional Process to cardiac interbeats intervals, in: J. Soc. Fr. Stat., 2009, vol. 150, n^o 1, pp. 54–72.
• 4O. Barrière, A. Echelard, J. Lévy Véhel.
  Self-Regulating Processes, in: Electronic Journal of Probability, December 2012. [ DOI : 10.1214/EJP.v17-2010 ]
  http://hal.inria.fr/hal-00749742
• 5F. Chalot, Q. V. Dinh, E. Herbin, L. Martin, M. Ravachol, G. Rogé.
  Estimation of the impact of geometrical uncertainties on aerodynamic coefficients using CFD, in: 10th AIAA Non-Deterministic Approaches, Schaumburg, USA, April 2008.
• 6K. Daoudi, J. Lévy Véhel, Y. Meyer.
  Construction of continuous functions with prescribed local regularity, in: Journal of Constructive Approximation, 1998, vol. 014, n^o 03, pp. 349–385.
• 7Y. Deremaux, J. Négrier, N. Piétremont, E. Herbin, M. Ravachol.
  Environmental MDO and uncertainty hybrid approach applied to a supersonic business jet, in: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization conference, 2008, Victoria.
• 8A. Echelard, O. Barrière, J. Lévy Véhel.
  Terrain modelling with multifractional Brownian motion and self-regulating processes, in: ICCVG 2010, Warsaw, Poland, Lecture Notes in Computer Science, Springer, 2010, vol. 6374, pp. 342-351.
  http://hal.inria.fr/inria-00538907/en
• 9A. Echelard, J. Lévy Véhel.
  Self-regulating processes-based modeling for arrhythmia characterization, in: Imaging and Signal Processing in Health Care and Technology, Baltimore, USA, May 2012.
  http://hal.inria.fr/hal-00670064
• 10K. Falconer, R. Le Guével, J. Lévy Véhel.
  Localisable moving average stable and multistable processes, in: Stoch. Models, 2009, vol. 25, pp. 648–672.
• 11K. Falconer, J. Lévy Véhel.
  Multifractional, multistable, and other processes with prescribed local form, in: J. Theoret. Probab., 2008, vol. 119, pp. 2277–2311, DOI 10.1007/s10959-008-0147-9.
• 12L. J. Fermin, J. Lévy Véhel.
  Modeling patient poor compliance in in the multi-IV administration case with Piecewise Deterministic Markov Models, 2011, preprint.
• 13L. J. Fermin, J. Lévy Véhel.
  Variability and singularity arising from poor compliance in a pharmacodynamical model II: the multi-oral case, 2011, preprint.
• 14E. Herbin, B. Arras, G. Barruel.
  From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields, 2010, preprint.
• 15E. Herbin.
  From n parameter fractional brownian motions to n parameter multifractional brownian motions, in: Rocky Mountain Journal of Mathematics, 2006, vol. 36, n^o 4, pp. 1249–1284.
• 16E. Herbin, J. Jakubowski, M. Ravachol, Q. V. Dinh.
  Management of uncertainties at the level of global design, in: Symposium "Computational Uncertainties", RTO AVT-147, 2007, Athens.
• 17E. Herbin, J. Lebovits, J. Lévy Véhel.
  Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motion, in: preprint, 2011.
• 18E. Herbin, J. Lévy Véhel.
  Stochastic 2-microlocal analysis, in: Stochastic Proc. Appl., 2009, vol. 119, n^o 7, pp. 2277–2311.
  http://arxiv.org/abs/math.PR/0504551
• 19E. Herbin, E. Merzbach.
  A characterization of the set-indexed fractional Brownian motion, in: C. R. Acad. Sci. Paris, 2006, vol. Ser. I 343, pp. 767–772.
• 20E. Herbin, E. Merzbach.
  A set-indexed fractional brownian motion, in: J. of theor. probab., 2006, vol. 19, n^o 2, pp. 337–364.
• 21E. Herbin, E. Merzbach.
  The multiparameter fractional Brownian motion, in: Math everywhere, Berlin, Springer, 2007, pp. 93–101.
  http://dx.doi.org/10.1007/978-3-540-44446-6_8
• 22E. Herbin, E. Merzbach.
  Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion, in: J. of theor. probab., 2009, vol. 22, n^o 4, pp. 1010–1029.
• 23E. Herbin, E. Merzbach.
  The set-indexed Lévy process: Stationarity, Markov and sample paths properties, 2010, preprint.
• 24E. Herbin, A. Richard.
  Hölder regularity for set-indexed processes, 2011, forthcoming.
• 25K. Kolwankar, J. Lévy Véhel.
  A time domain characterization of the fine local regularity of functions, in: J. Fourier Anal. Appl., 2002, vol. 8, n^o 4, pp. 319–334.
• 26J. Lebovits, J. Lévy Véhel.
  Stochastic Calculus with respect to multifractional Brownian motion.
  http://hal.inria.fr/inria-00580196/en
• 27J. Lévy Véhel, C. Tricot.
  On various multifractal spectra, in: Fractal Geometry and Stochastics III, Progress in Probability, Birkhäuser, ISBN 376437070X, 9783764370701, 2004, vol. 57, pp. 23-42, C. Bandt, U. Mosco and M. Zähle (Eds), Birkhäuser Verlag.
• 28J. Lévy Véhel, R. Vojak.
  Multifractal Analysis of Choquet Capacities: Preliminary Results, in: Advances in Applied Mathematics, January 1998, vol. 20, pp. 1–43.
• 29R. Peltier, J. Lévy Véhel.
  Multifractional Brownian Motion, Inria, 1995, n^o 2645.
  http://hal.inria.fr/inria-00074045
• 30M. Ravachol, Y. Deremaux, Q. V. Dinh, E. Herbin.
  Uncertainties at the conceptual stage: Multilevel multidisciplinary design and optimization approach, in: 26th International Congress of the Aeronautical Sciences, 2008, Anchorage.
• 31F. Roueff, J. Lévy Véhel.
  A Regularization Approach to Fractional Dimension Estimation, in: Fractals'98, 1998, Malta.
• 32S. Seuret, J. Lévy Véhel.
  A time domain characterization of of 2-microlocal Spaces, in: J. Fourier Anal. Appl., 2003, vol. 9, n^o 5, pp. 472–495.

Publications of the year

Doctoral Dissertations and Habilitation Theses

• 33B. Arras.
  Around some selfsimilar processes with stationary increments, Ecole Centrale de Paris, December 2014.
  https://tel.archives-ouvertes.fr/tel-01108624
• 34A. Richard.
  Local regularity of some fractional Brownian fields, Ecole Centrale Paris, September 2014.
  https://tel.archives-ouvertes.fr/tel-01091243

Articles in International Peer-Reviewed Journals

• 35S. Corlay, J. Lebovits, J. Lévy Véhel.
  Multifractional Stochastic volatility models, in: Mathematical Finance, April 2014, vol. 24, n^o 2, pp. 364-402.
  https://hal.inria.fr/hal-00653150
• 36X. Fan, I. Grama, Q. Liu.
  A generalization of Cramér large deviations for martingales, in: C. R. Acad. Sci. Paris, Ser. I, September 2014, vol. 352, pp. 853-858.
  https://hal.archives-ouvertes.fr/hal-01069115
• 37X. Fan, I. Grama, Q. Liu.
  Exponential inequalities for martingales with applications, in: Electronic Journal of Probability, January 2015, vol. 20, pp. 1 - 22. [ DOI : 10.1214/EJP.v20-3496 ]
  https://hal.inria.fr/hal-01108032
• 38J. Lebovits, J. Lévy Véhel, E. Herbin.
  Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions, in: Stochastic Processes and their Applications, 2014, n^o 124, pp. 678-708.
  https://hal.inria.fr/hal-00653808
• 39J. Lebovits, J. Lévy Véhel.
  White noise-based stochastic calculus with respect to multifractional Brownian motion, in: Stochastics An International Journal of Probability and Stochastic Processes, 2014, vol. 86, n^o 1, pp. 87-124.
  https://hal.inria.fr/inria-00580196

Other Publications

• 40A. Echelard, J. Lévy Véhel, A. Philippe.
  Statistical estimation of a class of self-regulating processes, August 2014, To appear in Scandinavian Journal of Statistics.
  https://hal.inria.fr/hal-00868604
• 41X. Fan, J. Lévy Véhel.
  Multistable Lévy motions and their continuous approximations, January 2015.
  https://hal.archives-ouvertes.fr/hal-01110716
• 42R. Le Guével, J. Lévy Véhel.
  Hausdorff, Large Deviation and Legendre Multifractal Spectra of Lévy Multistable Processes, December 2014.
  https://hal.inria.fr/hal-01089482
• 43J. Lévy Véhel, P.-E. Lévy Véhel, V. Lévy Véhel.
  A Model Investigating Incentives for Illegal Cultural Goods Sharing Sites to Become Legal, January 2015.
  https://hal.inria.fr/hal-01103048

References in notes

• 44F. Baccelli, D. Hong.
  AIMD, Fairness and Fractal Scaling of TCP Traffic, in: INFOCOM'02, June 2002.
• 45A. Benassi, S. Jaffard, D. Roux.
  Elliptic Gaussian random processes, in: Rev. Mathemàtica Iberoamericana, 1997, vol. 13, n^o 1, pp. 19–90.
• 46J. Bony.
  Second microlocalization and propagation of singularities for semilinear hyperbolic equations, in: Conf. on Hyperbolic Equations and Related Topics, 1984, pp. 11–49, Kata/Kyoto,Academic Press, Boston.
• 47G. Brown, G. Michon, J. Peyrière.
  On the multifractal analysis of measures, in: J. Statist. Phys., 1992, vol. 66, n^o 3, pp. 775–790.
• 48ESReDA.
  Uncertainty in Industrial Practice, a Guide to Quantitative Uncertainty Management, Wiley, 2009.
• 49K. Falconer.
  The local structure of random processes, in: J. London Math. Soc., 2003, vol. 2, n^o 67, pp. 657–672.
• 50K. Falconer.
  The multifractal spectrum of statistically self-similar measures, in: J. Theor. Prob., 1994, vol. 7, pp. 681–702.
• 51A. Goldberger, L. A. N. Amaral, J. Hausdorff, P. Ivanov, C. Peng, H. Stanley.
  Fractal dynamics in physiology: Alterations with disease and aging, in: PNAS, 2002, vol. 99, pp. 2466–2472.
• 52P. Ivanov, L. A. N. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Struzik, H. Stanley.
  Multifractality in human heartbeat dynamics, in: Nature, June 1999, vol. 399.
• 53S. Jaffard.
  Pointwise smoothness, two-microlocalization and wavelet coefficients, in: Publ. Mat., 1991, vol. 35, n^o 1, pp. 155–168.
• 54H. Kempka.
  2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability, in: Rev. Mat. Complut., 2009, vol. 22, n^o 1, pp. 227–251.
• 55M. B. Marcus, J. Rosen.
  Markov Processes, Gaussian Processes and Local Times, Cambridge University Press, 2006.
• 56G. Samorodnitsky, M. Taqqu.
  Stable Non-Gaussian Random Processes, Chapman and Hall, 1994.
• 57S. Stoev, M. Taqqu.
  Stochastic properties of the linear multifractional stable motion, in: Adv. Appl. Probab., 2004, vol. 36, pp. 1085–1115.