Alexandre RICHARD

Maître de conférences
Université Paris-Saclay
CentraleSupélec

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

Research interests

  1. Stochastic analysis;
  2. Stochastic/Rough Differential Equations, fractional Brownian motion;
  3. Interacting particle systems and Fokker-Planck PDEs with singular interaction.

Preprints

  1. Numerical approximation of SDEs with fractional noise and distributional drift, with L. Goudenège and E. M. Haress.
    2. Preprint, 2023. arXiv
  2. Quantitative approximation of the Burgers and Keller-Segel equations by moderately interacting particles, with C. Olivera and M. Tomasevic.
    3. Preprint, 2022. arXiv
  3. Long time Hurst regularity of fractional SDEs and their ergodic means, with E. M. Haress.
    4. Preprint, 2022. arXiv
  4. Lipschitz continuity in the Hurst parameter of functionals of stochastic differential equations driven by a fractional Brownian motion, with D. Talay.
    5. Preprint, 2021. arXiv

Publications

  1. Estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise, with E. M. Haress.
    2. Stat. Inference Stoch. Process. (accepted), 2024. arXiv
  2. Regularisation by fractional noise for one-dimensional differential equations with distributional drift, with L. Anzeletti and E. Tanré.
    3. Electron. J. Probab. 28, article no. 135, 1-49, 2023. DOI arXiv
  3. On the discrete-time simulation of the rough Heston model, with X. Tan and F. Yang.
    4. SIAM J. Fin. Math. 14(1):223-249, 2023. DOI arXiv
  4. Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel, with C. Olivera and M. Tomasevic.
    5. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XXIV: 691-749, 2023. DOI arXiv
  5. Discrete-time simulation of stochastic Volterra equations, with X. Tan and F. Yang.
    6. Stochastic Process. Appl. 141:109-138, 2021. DOI arXiv
  6. On the Root solution to the Skorokhod embedding problem given full marginals, with X. Tan and N. Touzi.
    7. SIAM J. Control Optim. 58(4):1874-1892, 2020. DOI arXiv
  7. Penalisation techniques for one-dimensional reflected rough differential equations, with E. Tanré and S. Torres.
    8. Bernoulli 26(4):2949-2986, 2020. DOI arXiv
  8. Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift, with F. Panloup.
    9. Electron. J. Probab. 25, article no. 62, 1-43, 2020. DOI arXiv
  9. An integrate-and-fire model to generate spike trains with long-range dependence, with P. Orio and E. Tanré.
    10. J. Comput. Neurosci. 44(3):297-312, 2018. DOI arXiv
  10. Noise sensitivity of functionals of stochastic differential equations driven by fractional Brownian motion: Results and perspectives, with D. Talay.
    11. 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
  12. Increment stationarity of L2-indexed stochastic processes: spectral representation and characterization.
    13. Electron. Commun. Probab. 21(paper 31):1-15, 2016. DOI
  13. Local Hölder regularity of set-indexed processes, with E. Herbin.
    14. Israel J. Math. 215(1):397-440, 2016. DOI arXiv
  14. A fractional Brownian field indexed by L2 and a varying Hurst parameter.
    15. Stochastic Process. Appl. 125(4):1394-1425, 2015. DOI arXiv

Supervision

  1. Thomas CAVALLAZZI (Lecteur Hadamard, 2023-...), co-supervised with M. Tomasevic.
  2. El Mehdi HARESS (PhD, 2021-...), co-supervised with L. Goudenège.
  3. Lukas ANZELETTI (PhD, 2020-2023), co-supervised with E. Tanré. Now post-doc at TU Vienna.

Ongoing research grants

  1. ANR-FAPESP project SDAIM (2023-2027, PI: F. Russo)
  2. ANR project SIMALIN (2019-2023, PI: L. Goudenège)

Recent and upcoming talks

  1. Workshop on Fractional Brownian Motion and its Applications, Luxembourg, April 2024.
  2. Conference on Stochastic Dynamics and Stochastic Equations, EPFL, March 2024.
  3. Séminaire de probabilités et statistique, Nice, March 2024.
  4. Séminaire de probabilités, Toulouse, January 2024.
  5. Conference on Mean field interactions with singular kernels and their approximations, Paris, December 2023.
  6. Séminaire de probabilités et mathématiques financières, Evry, November 2023.
  7. A Random Walk in the Land of Stochastic Analysis and Numerical Probability Conference (CIRM, link), September 2023.
  8. Journées de Probabilités, Angers, June 2023.
  9. Séminaire MICS, CentraleSupélec, December 2022.
  10. Journées trajectoires rugueuses et méthodes numériques, Pau, December 2022.
  11. Conférence du GdR TRAG, Nanterre, May 2022.
  12. Stochastic models and finance seminar, Cermics (Ecole des Ponts), February 2022.
  13. XIII Summer Workshop in Mathematics, Brasilia (Brasil), February 2021.
  14. Séminaire de probabilités et statistique, Lille, February 2020.
  15. Workshop "Asymptotic expansion and Malliavin calculus II", Paris, December 2019.
  16. Conférence du GdR TRAG, Nancy, October 2019.
  17. First joint meeting Brazil-France in mathematics IMPA (Brasil), July 2019.
  18. Workshop in stochastic analysis and applications, Unicamp (Brasil), July 2019.
  19. Rencontres Mathématiques de Rouen, June 2018.
  20. International Conference on Mathematical Neuroscience, Juan-les-Pins, June 2018.
  21. Séminaire Bachelier (Paris), May 2018.
  22. Séminaire Probabilités-Statistiques-Contrôle (ENSTA-CMAP-ENSAE), January 2018.

Organisation of conferences

  1. With C. Olivera, F. Russo and M. Tomasevic, we organized a winter school held at CIRM (Marseille) on Stochastic and Deterministic Analysis for Irregular Models in January 2024.

  2. With P. Lafitte, we organized the conférence d'inauguration de la Fédération de Mathématiques de CentraleSupélec, in November 2022.

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

  4. 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, 2020-2024.
  2. Convergence, Integration, Probability (lectures and labs), CentraleSupélec 1st year, 2018-2024.
  3. Complex analysis (lectures), CentraleSupélec 1st year, 2017-2021.
  4. Partial Differential Equations (some lectures and labs), CentraleSupélec 1st year, 2018-2021, 2022-2024.
  5. Distributions et opérateurs (labs), CentraleSupélec 2nd year, 2017-2024.
  6. Probabilités avancées (labs), CentraleSupélec 2nd year, 2019-2020.
  7. Analysis, Probability (labs), CentraleSupélec 1st year, 2017-2018.