Alexandre RICHARD

Maître de conférences (lecturer)
Laboratoire MICS et Fédération de Mathématiques CNRS 3487, CentraleSupélec, Université Paris-Saclay

E-mail: alexandre'dot'richard'at'centralesupelec'dot'fr

Research interests

  1. Stochastic analysis;
  2. Stochastic Differential Equations, Rough Differential Equations;
  3. Fractional Brownian motion, fractional processes.

Preprints

  1. Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel, with C. Olivera and M. Tomasevic.
  2. Preprint, 2020. arXiv:2011.00537
  3. Particle approximation of the 2-d parabolic-elliptic Keller-Segel system in the subcritical regime, with C. Olivera and M. Tomasevic.
  4. Preprint, 2020. arXiv:2004.03177
  5. Discrete-time simulation of stochastic Volterra equations, with X. Tan and F. Yang.
  6. Preprint, 2020. arXiv:2004.00340
  7. Hölder continuity in the Hurst parameter of functionals of Stochastic Differential Equations driven by fractional Brownian motion, with D. Talay.
  8. Preprint, 2016. arXiv:1605.03475

Publications

  1. On the Root solution to the Skorokhod embedding problem given full marginals, with X. Tan and N. Touzi.
  2. SIAM J. Control Optim. 58(4):1874-1892, 2020. DOI arXiv
  3. Penalisation techniques for one-dimensional reflected rough differential equations, with E. Tanré and S. Torres.
  4. Bernoulli 26(4):2949-2986, 2020. DOI arXiv
  5. Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift, with F. Panloup.
  6. Electron. J. Probab. 25(paper 62):1-43, 2020. DOI arXiv
  7. An integrate-and-fire model to generate spike trains with long-range dependence, with P. Orio and E. Tanré.
  8. J. Comput. Neurosci. 44(3):297-312, 2018. DOI arXiv
  9. Noise sensitivity of functionals of stochastic differential equations driven by fractional Brownian motion: Results and perspectives, with D. Talay.
  10. In Modern Problems of Stochastic Analysis and Statistics: Selected Contributions in Honor of Valentin Konakov, Ed. V. Panov, Springer Proceedings in Mathematics & Statistics (vol. 208), 2017. DOI arXiv
  11. Some singular sample path properties of a multiparameter fractional Brownian motion.
  12. J. Theoret. Probab. 30: 1285-1309, 2017. DOI arXiv
  13. Increment stationarity of L2-indexed stochastic processes: spectral representation and characterization.
  14. Electron. Commun. Probab. 21(paper 31):1-15, 2016. DOI
  15. Local Hölder regularity of set-indexed processes, with E. Herbin.
  16. Israel J. Math. 215(1):397-440, 2016. DOI arXiv
  17. A fractional Brownian field indexed by L2 and a varying Hurst parameter.
  18. Stochastic Process. Appl. 125(4):1394-1425, 2015. DOI arXiv


    (You can also find my PhD thesis here).

Recent talks and seminars

  1. February 2021, XIII Summer Workshop in Mathematics (Brasilia, link).
  2. February 2020, Séminaire de probabilités et statistique, Université de Lille.
  3. December 2019, Workshop "Asymptotic expansion and Malliavin calculus II" (Paris, link).
  4. October 2019, Conférence du GdR TRAG (Nancy, link).
  5. July 2019, First joint meeting Brazil-France in mathematics (IMPA, link).
  6. July 2019, Workshop in stochastic analysis and applications (Unicamp, link).
  7. June 2018, Rencontres Mathématiques de Rouen, Convergence to equilibrium for Gaussian-driven SDEs.
  8. June 2018, International Conference on Mathematical Neuroscience (Juan-les-Pins), Long-range dependence in spike trains.
  9. May 2018, Séminaire Bachelier (Paris), Convergence to equilibrium for Gaussian-driven SDEs.
  10. January 2018, Ensta, Séminaire Probabilités-Statistiques-Contrôle (ENSTA-CMAP-ENSAE).

Organisation of conferences

  1. With C. Bauzet, C.-E. Bréhier, J. Charrier and L. Goudenège, we organize the NASPDE workshop that will be held at CIRM (Marseille) in November 2021:
    Numerical Analysis of Stochastic Partial Differential Equations.

  2. With N. Marie and F. Panloup, we organized a workshop in November 2019, in CentraleSupélec:
    The long-time behaviour and statistical inference for stochastic processes: from Markovian to long-memory dynamics.

Teaching

  1. Limit theorems, CentraleSupélec 3rd year, 2020-2021.
  2. Convergence, Integration, Probability (lectures and labs), CentraleSupélec 1st year, 2018-2021.
  3. Complex analysis (lectures), CentraleSupélec 1st year, 2017-2021.
  4. Partial Differential Equations (some lectures and labs), CentraleSupélec 1st year, 2018-2021.
  5. Distributions et opérateurs (labs), CentraleSupélec 2nd year, 2017-2021.
  6. Probabilités avancées (labs), CentraleSupélec 2nd year, 2019-2020.
  7. Analysis, Probability (labs), CentraleSupélec 1st year, 2017-2018.