Publications

ArXiv papers

 

Works in progress...


Over the last few years, I've spent a lot of time writing the following books with Pauline Lafitte:
  • [with P. Lafitte], Modern mathematical concepts for the engineer. Part I - From infinitesimal calculus to the measure theory, World Scientific, to appear.
  • [with P. Lafitte], Modern mathematical concepts for the engineer. Part II - Consequences for mathematical modeling, World Scientific, in preparation.
These books are the fruit of many years of teaching the entire CentraleSupélec class (see my teaching page). It has also been enriched by several years of reflection on the teaching of mathematics in an engineering curriculum.

I also spent a lot of time working on the following article, including the consequences of its results:
  • Local regularity and Hausdorff dimension of time-changed Brownian motions, in preparation.
  • Locally asymptotic self-similarity and Hölder regularity, in preparation.

 

Books and Book Chapters


  • [with Y. Xiao], Sample Paths Properties of the Set-Indexed Fractional Brownian Motion, ResearchGate, In: Aldroubi, A., Cabrelli, C., Jaffard, S., Molter, U. (eds) New Trends in Applied Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. DOI, 2019.

Journal papers


  • [with B. Hannebicque], Regularity of an abstract Wiener integral, arXiv:2006.06060 [math.PR], Stoch. Proc. and their Appl., Vol. 154, 154-196, 2022.
  • [with A. Richard], Local Hölder regularity for set-indexed processes, arXiv:1203.0750 [math.PR], Israel J. of Math., Vol. 215(1), 397-440, 2016.
  • [with J. Lebovits and J. Lévy-Véhel], Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions, Stoch. Proc. and their Appl., Vol. 124, 678-708, 2014.
  • [with B. Arras and G. Barruel], From almost sure regularity to almost sure Hausdorff dimension for Gaussian fields, arXiv:1206.0605 [math.PR], ESAIM Probability and Statistics, Vol. 18, 418-440, 2014.
  • [with E. Merzbach], The set-indexed Lévy process: Stationarity, Markov and sample paths properties, arXiv:1108.0873 [math.PR], Stoch. Proc. and their Appl., Vol. 123, 1638-1670, 2013.
  • [with P. Balanca], A set-indexed Ornstein-Uhlenbeck process, arXiv:1203.5524 [math.PR], Electron. Commun. Probab., 17, no. 39, 1-14, 2012.
  • [with P. Balanca], 2-microlocal analysis of martingales and stochastic integrals, arXiv:1107.6016 [math.PR], Stoch. Proc. and their Appl., Vol. 122, 2346-2382, 2012.
  • [with J. Lévy-Véhel], Stochastic 2-microlocal analysis, arXiv:math/0504551 [math.PR], Stoch. Proc. and their Appl., Vol. 119, 2277-2311, 2009.
  • [with E. Merzbach], Stationarity and self-similarity characterization of the set-indexed fractional Brownian motion, arXiv:0706.3472 [math.PR], J. of Theor. Probab., Vol. 22(4), 1010-1029, 2009.
  • [with E. Merzbach], A characterization of the set-indexed fractional Brownian motion by increasing paths, arXiv:math/0607575 [math.PR], C. R. Acad. Sci. Paris, Ser. I 343, 767-772, 2006.
  • From N-parameter fractional Brownian motions to N-parameter multifractional Brownian motions, arXiv:math/0503182 [math.PR], Rocky Mountain J. of Math., Volume 36-4, 1249-1284, 2006.

 

Conference papers


  • [with Y. Deremaux, J. Négrier, N. Piétremont and M. Ravachol], Environmental MDO and uncertainty hybrid approach applied to a supersonic business jet, In: 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization conference, Victoria 2008.
  • [with Y. Deremaux, Q. V. Dinh and M. Ravachol], Uncertainties at the conceptual stage: Multilevel multidisciplinary design and optimization approach, In: 26th International Congress of the Aeronautical Sciences, Anchorage 2008.
  • [with F. Chalot, Q. V. Dinh, L. Martin, M. Ravachol and G. Rogé], Estimation of the impact of geometrical uncertainties on aerodynamic coefficients using CFD, In: 10th AIAA Non-Deterministic Approaches Conference, Schaumburg 2008.
  • [with J. Jakubowski, M. Ravachol and Q.V. Dinh], Management of uncertainties at the level of global design, In: Symposium "Computational Uncertainty" RTO AVT-147, Athens 2007.
  • [with E. Merzbach], The Multiparameter fractional Brownian motion, arXiv:math/0605279 [math.PR], in: Math Everywhere; G. Aletti, M. Burger, A. Micheletti, D. Morale (Eds.), Springer 2006.