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, in: Submitted, 2011, submitted.
• 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, submitted.
  
  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

Articles in International Peer-Reviewed Journals

• 33E. Herbin, B. Arras, G. Barruel.
  
  From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields, in: ESAIM: Probability and Statistics, 2013, 28 p.
  
  http://hal.inria.fr/hal-00862543
• 34R. Le Guével, J. Lévy Véhel, L. Liu.
  
  On two multistable extensions of stable Lévy motion and their semi-martingale representations, in: Journal of Theoretical Probability, November 2013. [ DOI : 10.1007/s10959-013-0528-6 ]
  
  http://hal.inria.fr/hal-00868607
• 35J. 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, To appear.
  
  http://hal.inria.fr/hal-00653808
• 36J. Lévy Véhel.
  
  Beyond multifractional Brownian motion: new stochastic models for geophysical modelling, in: Nonlinear Processes in Geophysics, January 2013.
  
  http://hal.inria.fr/hal-00875268
• 37P.-E. Lévy Véhel, J. Lévy Véhel.
  
  Variability and singularity arising from poor compliance in a pharmacokinetic model I: the multi-IV case, in: Journal of Pharmacokinetics and Pharmacodynamics, January 2013, vol. 40, n^o 1, pp. 15-39, To appear.
  
  http://hal.inria.fr/hal-00752114
• 38J. Lévy Véhel, F. Mendivil.
  
  Christiane's Hair, in: American Mathematical Monthly, November 2013, vol. 120, n^o 9, pp. 771-786, To appear.
  
  http://hal.inria.fr/hal-00744268
• 39J. Lévy Véhel, M. Rams.
  
  Large Deviation Multifractal Analysis of a Class of Additive Processes with Correlated Non-Stationary Increments, in: IEEE/ACM Transactions on Networking, November 2013, vol. 21, n^o 4, pp. 1309-1321, Accepted for publication.
  
  http://hal.inria.fr/inria-00633195

Conferences without Proceedings

• 40H. El Mekeddem, J. Lévy Véhel.
  
  Value at Risk with tempered multistable motions, in: 30th International French Finance Association Conference, Lyon, France, May 2013.
  
  http://hal.inria.fr/hal-00868634
• 41J. Lévy Véhel.
  
  Financial modelling with tempered multistable motions, in: International Workshop on Statistical modeling, financial data analysis and applications, Venise, Italy, November 2013.
  
  http://hal.inria.fr/hal-00879759

Other Publications

• 42B. Arras.
  
  A white noise approach to stochastic integration with respect to the Rosenblatt process, 2013.
  
  http://hal.inria.fr/hal-00862330
• 43A. Echelard, J. Lévy Véhel.
  
  Local Regularity Preserving Signal Denoising I: Hölder Exponents, November 2013, submitted.
  
  http://hal.inria.fr/hal-00879754
• 44A. Echelard, J. Lévy Véhel, A. Philippe.
  
  Statistical estimation of a class of self-regulating processes, October 2013, Submitted.
  
  http://hal.inria.fr/hal-00868604
• 45L. J. Fermin, J. Lévy Véhel.
  
  Variability and singularity arising from poor compliance in a pharmacokinetic model II: the multi-oral case, October 2013, submitted.
  
  http://hal.inria.fr/hal-00868621
• 46A. Richard.
  
  A fractional Brownian field indexed by $L⌃2$ and a varying Hurst parameter, 2013, submitted.
  
  http://hal.inria.fr/hal-00922028

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  Continuous Gaussian multifractional processes with random pointwise Hölder regularity, in: J. Theoret. Probab., 2013, vol. 26, n^o 1, pp. 72–93.
  
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• 49F. Baccelli, D. Hong.
  
  AIMD, Fairness and Fractal Scaling of TCP Traffic, in: INFOCOM'02, June 2002.
• 50P. Balança.
  
  Sample path properties of irregular multifractional Brownian motion, in: Preprint, 2013.
• 51A. Benassi, S. Jaffard, D. Roux.
  
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• 54G. Brown, G. Michon, J. Peyrière.
  
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• 62G. Ivanoff, E. Merzbach.
  
  Set-Indexed Martingales, Chapman & Hall/CRC, 2000.
• 63P. Ivanov, L. A. N. Amaral, A. Goldberger, S. Havlin, M. Rosenblum, Z. Struzik, H. Stanley.
  
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  2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability, in: Rev. Mat. Complut., 2009, vol. 22, n^o 1, pp. 227–251.
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  A probabilistic approach for the evaluation of pharmacological effect induced by patient irregular drug intake, in: J. Pharmacokinet. Pharmacodyn., 2009, vol. 36, n^o 3, pp. 221–238.
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  Markov Processes, Gaussian Processes and Local Times, Cambridge University Press, 2006.
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• 71G. Samorodnitsky, M. Taqqu.
  
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  Stochastic properties of the linear multifractional stable motion, in: Adv. Appl. Probab., 2004, vol. 36, pp. 1085–1115.
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  Analysis of the Rosenblatt process, in: ESAIM Probab. Stat., 2008, vol. 12, pp. 230–257.
  
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• 74B. Vrijens, J. Urquhart.
  
  New findings about patient adherence to prescribed drug dosing regimens: an introduction to pharmionics, in: Eur. J. Hosp. Pharm. Sci., 2005, vol. 11, n^o 5, pp. 103–106.
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