DEYA Aurélien

Publications:

• • A. Deya and S. Tindel: Rough Volterra equations 1: The algebraic integration setting. Stoch. Dyn., 9(3): 437-477, 2009.
  • A. Deya and S. Tindel: Rough Volterra equations 2: convolutional generalized integrals. Stoch. Process. Appl., 121(8): 1864-1899, 2011.
  • A. Deya: A discrete approach to rough parabolic equations. Electron. J. Probab., 16: 1489-1518, 2011.
  • A. Deya, M. Gubinelli, and S. Tindel: Non-linear rough heat equations. Probab. Theory Related Fields, 153(1-2): 97-147, 2012.
  • A. Deya, A. Neuenkirch, and S. Tindel: A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion. Ann. Inst. H. Poincaré Probab. Statist., 48(2): 518-550, 2012.
  • A. Deya: Numerical schemes for rough parabolic equations. Appl. Math. Optim., 65(2): 253-292, 2012.
  • A. Deya and I. Nourdin: Convergence of Wigner integrals to the tetilla law. ALEA, Lat. Am. J. Probab. Math. Stat., 9: 101-127, 2012.
  • A. Deya and S. Tindel: Malliavin calculus for fractional heat equation. In Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart. Springer Proceedings in Mathematics and Statistics, 34: 361-384, 2013.
  • A. Deya, S. Noreddine and I. Nourdin: Fourth moment theorem and q-Brownian chaos. Comm. Math. Phys., 321(1): 113-134, 2013.
  • A. Deya, M. Jolis and L. Quer-Sardanyons: The Stratonovich heat equation: a continuity result and weak approximations. Electron. J. Probab., 18(3): 1-34, 2013.
  • A. Deya and R. Schott: On the rough paths approach to non-commutative stochastic calculus. J. Funct. Anal., 265(4): 594-628, 2013.
  • A. Deya and I. Nourdin: Invariance principles for homogeneous sums of free random variables. Bernoulli, 20(2): 395-1028, 2014.
  • A. Deya, D. Nualart and S. Tindel: On $L^2$ modulus of continuity of Brownian local times and Riesz potentials. Ann. Probab., 43(3): 1493-1534, 2015.
  • A. Deya: On a modelled rough heat equation. Probab. Theory Related Fields, 166(1): 1-65, 2016.
  • A. Deya: Construction and Skorohod representation of a fractional K-rough path. Electron. J. Probab., 22, 2017.
  • A. Deya and R. Schott: On stochastic calculus with respect to q-Brownian motion. J. Funct. Anal., 274(4): 1047-1075, 2018.
  • A. Deya and R. Schott: On multiplication in $q$-Wiener chaoses. Electron. Commun. Probab., 23, 2018.
  • A. Deya, F. Panloup and S. Tindel: Rate of convergence to equilibrium of fractional driven stochastic differential equations with rough multiplicative noise (with supplement). Ann. Probab., 47(1): 464-518, 2019.
  • A. Deya and R. Schott: Integration with respect to the non-commutative fractional Brownian motion (with supplement). Bernoulli, 25(3): 2137-2162, 2019.
  • A. Deya: A non-linear wave equation with fractional perturbation (corrected version). Ann. Probab., 47(3): 1775-1810, 2019.
  • A. Deya, M. Gubinelli, M. Hofmanova and S. Tindel: One-dimensional reflected rough differential equations. Stochastic Process. Appl., 129(9), 3261-3281, 2019.
  • A. Deya, M. Gubinelli, M. Hofmanova and S. Tindel: A priori estimates for rough PDEs with application to rough conservation laws. J. Funct. Anal., 276(12), 3577-3645, 2019.
  • A. Deya: Integration with respect to the Hermitian fractional Brownian motion. J. Theoret. Probab., 33(1), 295-318, 2020.
  • A. Deya: On a non-linear 2D fractional equation. Ann. Inst. H. Poincaré Probab. Statist., 56(1), 477-501, 2020.
  • X. Chen, A. Deya, C. Ouyang and S. Tindel: A $K$-rough path above the space-time fractional Brownian motion. Stochastics and Partial Differential Equations: Analysis and Computations, 9 (2021), no. 4, 819-866.
  • A. Deya and R. Schott: Skorohod and rough integration with respect to the non-commutative fractional Brownian motion. ALEA Lat. Am. J. Probab. Math. Stat., 18 (2021), 907-943.
  • X. Chen, A. Deya, C. Ouyang and S. Tindel: Moment estimates for some renormalized parabolic Anderson models. Ann. Probab., 49 (2021), no. 5, 2599-2636.
  • A. Deya, N. Schaeffer and L. Thomann: A nonlinear Schrödinger equation with fractional noise. Trans. Amer. Math. Soc., 374 (2021), no. 6, 4375-4422.
  • A. Deya. On ill-posedness of nonlinear stochastic wave equations driven by rough noise. Stochastic Process. Appl., 150 (2022), 215-249.
  • A. Deya and R. Marty: A full discretization of the rough fractional linear heat equation. Electron. J. Probab., 27 (2022), Article No. 122, 1-41.
  • X. Chen, A. Deya, J. Song and S. Tindel: Hyperbolic Anderson model 2: Strichartz estimates and Stratonovich setting. Int. Math. Res. Not. IMRN, 21 (2023), 18575-18628.
  • X. Chen, A. Deya, J. Song and S. Tindel: Solving the hyperbolic Anderson model 1: Skorohod setting. Ann. Inst. H. Poincaré Probab. Statist., 61 (2025), no. 3, 1794-1814.
  • A. Deya: On the 1d stochastic Schrödinger product. Stochastics and Partial Differential Equations: Analysis and Computations, 13 (2025), 1451-1501.
  • A. Deya, R. Fukuizumi and L. Thomann: Renormalization of a 1d quadratic Schrödinger model with additive noise. Ann. Probab., in press.

Prépublications:

• A. Deya, R. Fukuizumi and L. Thomann: On the parabolic $\Phi^4_3$ model for the harmonic oscillator: diagrams and local existence. Arxiv preprint, 115 p., 2025.
• A. Deya, R. Fukuizumi and L. Thomann: On the parabolic $\Phi^4_3$ model for the harmonic oscillator: global existence and invariant measure. In preparation.

Cours M2 MFA: Introduction aux EDPs stochastiques 2018-2019

Cours M2 MFA: Introduction aux EDPs stochastiques 2020-2021

Né le 13 septembre 1983 à Nancy.
Tétraplégique depuis l’adolescence à la suite d’un accident.

Poste actuel
Depuis octobre 2013: chargé de recherche CNRS à Nancy, dans l’équipe Probabilités et Statistiques de l’institut Elie Cartan de Lorraine (UMR 7502).

Cursus

• 2012-2013: CDD de chargé de recherche CNRS
• 2010-2012: Contrat post-doctoral CNRS
• 2007-2010: Contrat doctoral CNRS
• Juin 2007: Master 2 de Mathématiques, parcours « Probabilités et Statistiques », Université Henri Poincaré de Nancy, mention Très Bien.

Thèse
Etude de systèmes différentiels fractionnaires, préparée sous la direction du Professeur Samy Tindel et soutenue publiquement le 18 octobre 2010 devant un jury composé de:

• Arnaud Debussche, Professeur, ENS Cachan (Rapporteur)
• Massimiliano Gubinelli, Professeur, Paris Dauphine
• Michel Ledoux, Professeur, Toulouse
• Antoine Lejay, CR Inria, Nancy
• Ivan Nourdin, Professeur, Nancy
• Marta Sanz-Solé, Professeur, Barcelone (Rapporteuse)
• Samy Tindel, Professeur, Nancy (Directeur de thèse)

Sélection sur les cinq dernières années:

• Probabilistic Operator Algebra Seminar, Berkeley, 2021.
• Columbia SPDE seminar, New York, 2021.
• Computational and Applied Mathematics seminar, Chalmers, 2021.
• Conference on Mathematics of Wave Phenomena, Karlsruhe, 2022.
• Conference on Stochastic Analysis and Stochastic Partial Differential Equations, Barcelone, 2022.
• Nonlinear and Random Waves, RIMS Kyoto, 2022.
• Stochastic Analysis seminar, Imperial College London, 2023.
• Workshop on Stochastic Dynamics and Stochastic Equations, EPFL Lausanne, 2024.
• Probability and interactions, Tokyo Waseda, 2025.
• Emerging Synergies between Stochastic Analysis and Statistical Mechanics, Banff, 2025.