Alexandre RICHARD

Research Interests

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

Publications

Preprints

• Numerical approximation of the stochastic heat equation with a distributional reaction term, with L. Goudenège and E. M. Haress.
Preprint, 2024. arXiv
• Quantitative approximation of the Burgers and Keller-Segel equations by moderately interacting particles, with C. Olivera and M. Tomasevic.
Preprint, 2022. arXiv

Publications

• Numerical approximation of SDEs with fractional noise and distributional drift, with L. Goudenège and E. M. Haress.
Stochastic Process. Appl. 181, 2025. DOI arXiv
• Long time Hurst regularity of fractional SDEs and their ergodic means, with E. M. Haress.
J. Theoret. Probab. 38, paper no. 24, 2025. DOI arXiv
• Estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise, with E. M. Haress.
Stat. Inference Stoch. Process. 27: 641-691, 2024. DOI arXiv
• Lipschitz continuity in the Hurst parameter of functionals of stochastic differential equations driven by a fractional Brownian motion, with D. Talay.
Electron. J. Probab. 29, paper no. 135, 1-70, 2024. DOI arXiv
• Regularisation by fractional noise for one-dimensional differential equations with distributional drift, with L. Anzeletti and E. Tanré.
Electron. J. Probab. 28, paper no. 135, 1-49, 2023. DOI arXiv
• On the discrete-time simulation of the rough Heston model, with X. Tan and F. Yang.
SIAM J. Fin. Math. 14(1):223-249, 2023. DOI arXiv
• Quantitative particle approximation of nonlinear Fokker-Planck equations with singular kernel, with C. Olivera and M. Tomasevic.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XXIV: 691-749, 2023. DOI arXiv
• Discrete-time simulation of stochastic Volterra equations, with X. Tan and F. Yang.
Stochastic Process. Appl. 141:109-138, 2021. DOI arXiv
• On the Root solution to the Skorokhod embedding problem given full marginals, with X. Tan and N. Touzi.
SIAM J. Control Optim. 58(4):1874-1892, 2020. DOI arXiv
• Penalisation techniques for one-dimensional reflected rough differential equations, with E. Tanré and S. Torres.
Bernoulli 26(4):2949-2986, 2020. DOI arXiv
• Sub-exponential convergence to equilibrium for Gaussian driven Stochastic Differential Equations with semi-contractive drift, with F. Panloup.
Electron. J. Probab. 25, paper no. 62, 1-43, 2020. DOI arXiv
• An integrate-and-fire model to generate spike trains with long-range dependence, with P. Orio and E. Tanré.
J. Comput. Neurosci. 44(3):297-312, 2018. DOI arXiv
• Noise sensitivity of functionals of stochastic differential equations driven by fractional Brownian motion: Results and perspectives, with D. Talay.
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
• Some singular sample path properties of a multiparameter fractional Brownian motion.
J. Theoret. Probab. 30: 1285-1309, 2017. DOI arXiv
• Increment stationarity of L²-indexed stochastic processes: spectral representation and characterization.
Electron. Commun. Probab. 21(paper 31):1-15, 2016. DOI
• Local Hölder regularity of set-indexed processes, with E. Herbin.
Israel J. Math. 215(1):397-440, 2016. DOI arXiv

• A fractional Brownian field indexed by L² and a varying Hurst parameter.
Stochastic Process. Appl. 125(4):1394-1425, 2015. DOI arXiv

Supervision

• Nicoleta CAZACU (PhD, 2024-...), co-supervised with M. Tomasevic.
  
• Thomas CAVALLAZZI (Lecteur Hadamard, 2023-...), co-supervised with M. Tomasevic.
  
• El Mehdi HARESS (PhD, 2021-2024), co-supervised with L. Goudenège. Now post-doc at University of Leeds.
  
• Lukas ANZELETTI (PhD, 2020-2023), co-supervised with E. Tanré. Now post-doc at TU Vienna.
  

Grants (ongoing)

• MathAmSud project, Explore-SDE (2025-2027, PIs: S. Torres, E. Tanré)
• ANR-FAPESP project SDAIM (2023-2027, PI: F. Russo)
  

Conferences

Recent and upcoming talks

• Conference on New trends of stochastic nonlinear systems: well-posedeness, dynamics ans numerics, CIRM, October 2025.
• Workshop on Irregular Stochastic Analysis, Cortona, June 2025.
• Conference of the Romanian probability and statistics society, Bucharest, May 2025.
• Workshop on regularisation by noise, Vienna, April 2025.
• Séminaire de probabilités et statistique, Université Gustave Eiffel, November 2024.
• Conférence du GdR TRAG, Nice, July 2024.
• PDE seminar, UniCamp (Brazil), May 2024.
• Workshop on Fractional Brownian Motion and its Applications, Luxembourg, April 2024.
• Conference on Stochastic Dynamics and Stochastic Equations, EPFL, March 2024.
• Séminaire de probabilités et statistique, Nice, March 2024.
• Séminaire de probabilités, Toulouse, January 2024.
• Conference on Mean field interactions with singular kernels and their approximations, Paris, December 2023.
• Séminaire de probabilités et mathématiques financières, Evry, November 2023.
• A Random Walk in the Land of Stochastic Analysis and Numerical Probability Conference, CIRM, September 2023.
• Journées de Probabilités, Angers, June 2023.
• Séminaire MICS, CentraleSupélec, December 2022.
• Journées trajectoires rugueuses et méthodes numériques, Pau, December 2022.
• Conférence du GdR TRAG, Nanterre, May 2022.
• Stochastic models and finance seminar, Cermics (Ecole des Ponts), February 2022.
• XIII Summer Workshop in Mathematics, Brasilia (Brasil), February 2021.
• Séminaire de probabilités et statistique, Lille, February 2020.
• Workshop "Asymptotic expansion and Malliavin calculus II", Paris, December 2019.
• Conférence du GdR TRAG, Nancy, October 2019.
• First joint meeting Brazil-France in mathematics IMPA (Brasil), July 2019.
• Workshop in stochastic analysis and applications, Unicamp (Brasil), July 2019.

Organisation of conferences

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

Edition

• Member of the editorial committee for the proceedings of the CJC-MA conference, volume to be published in ESAIM:ProcS, 2025.
• Member of the editorial committee for the proceedings of the SDAIM winter school, 2025+.

Teaching

• Limit theorems, CentraleSupélec 3rd year, since 2020.
• Convergence, Integration, Probability (lectures and labs), CentraleSupélec 1st year, since 2018.
• Complex analysis (lectures), CentraleSupélec 1st year, 2017-2021.
• Partial Differential Equations (some lectures and labs), CentraleSupélec 1st year, 2018-2021, now since 2022.
• Distributions et opérateurs (labs), CentraleSupélec 2nd year, since 2017.
• Probabilités avancées (labs), CentraleSupélec 2nd year, 2019-2020.
• Analysis, Probability (labs), CentraleSupélec 1st year, 2017-2018.