===== Stéphane Menozzi======= {{:members:smenozzi:menozzi.jpg?200}} Professeur des universités \\ Université d'Évry Val d'Essonne \\ Laboratoire de Mathématiques et Modélisation d'Évry (UMR 8071) \\ I.B.G.B.I., 23 Bd. de France, 91037 Évry Cedex \\ Bureau 306 \\ ☎ +33 (0)1 64 85 34 98 \\ \\ ---- =====Thèmes de Recherche:===== * Analyse stochastique et Applications\\ ---- ===== Publications === * E. Gobet, S. Menozzi. [[http://www.cmap.polytechnique.fr/preprint/comment.php?showdetails=1&paper=503|"Exact Approximation rate of killed hypoelliptic diffusions using the discrete Euler scheme"]] , [[http://www.sciencedirect.com/science/article/pii/S0304414904000407|Stochastic Processes and Their Applications, 112-2 (2004), 201-223.]]\\ * F. Delarue, S. Menozzi. "A forward backward algorithm for quasi-linear PDEs". [[https://projecteuclid.org/euclid.aoap/1141654284|Annals of Applied Probability , 16-1 (2006), 140-184]].\\ * S. Menozzi. "[[http://www.cmap.polytechnique.fr/preprint/comment.php?showdetails=1&paper=568|Improved simulation of the killed Brownian motion in a cone"]]. [[http://epubs.siam.org/doi/abs/10.1137/050636966|SIAM Journal on Numerical Analysis, 44-6 (2006), 2610-2632]].\\ * E. Gobet, S. Menozzi. [[http://www.cmap.polytechnique.fr/preprint/comment.php?showdetails=1&paper=559|"Discrete Sampling of functionals of Itô processes"]]. [[https://link.springer.com/chapter/10.1007/978-3-540-71189-6_19|Séminaire de Probabilités, XL (2007), 355-375]].\\ * F. Delarue, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00021967v1|"An interpolated Stochastic Algorithm for Quasi-Linear PDEs"]]. [[http://www.ams.org/journals/mcom/2008-77-261/S0025-5718-07-02008-X/|Mathematics of Computation , 261-77 (2008), 125-158]].\\ * B. Bouchard, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00177481v2|"Strong Approximations of BSDEs in a domain"]]. [[https://projecteuclid.org/euclid.bj/1262962228|Bernoulli, 15-4 (2009), 1117-1147]].\\ * E. Gobet, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00157975v3|"Stopped diffusion processes: overshoots and boundary correction"]]. [[http://www.sciencedirect.com/science/article/pii/S0304414909001653|Stochastic Processes and Their Applications, 120-2 (2010), 130-162]].\\ * V. Konakov, S. Menozzi, S. Molchanov. [[https://hal.archives-ouvertes.fr/hal-00256588v2|"Explicit parametrix and local limit theorems for some degenerate diffusion processes"]]. [[https://projecteuclid.org/euclid.aihp/1288878329|Annales de l'Institut Henri Poincaré (Série B), 46-4 (2010), 908-923]].\\ * F. Delarue, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00436051v1|"Density Estimates for a Random Noise Propagating through a Chain of Differential Equations"]]. [[http://www.sciencedirect.com/science/article/pii/S0022123610001977|Journal of functional analysis, 259-6 (2010), 1577-1630]].\\ * V. Lemaire and S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00445494v1|"On some Non Asymptotic Bounds for the Euler Scheme"]]. [[https://projecteuclid.org/euclid.ejp/1464819838|Electronic Journal of Probability, Volume 15 (2010), 1645-1681]].\\ * V. Konakov, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00331845v3|"Weak Error for stable driven SDEs: expansion of the densities"]]. [[https://link.springer.com/article/10.1007/s10959-010-0291-x|Journal of Theoretical Probability, 24-2 (2011), 454-478]].\\ * S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00533300v1|"Parametrix techniques and martingale problems for some degenerate Kolmogorov equations"]]. [[https://projecteuclid.org/euclid.ecp/1465261979|Electronic Communications in Probability 16 (2011), 234-250]].\\ * V. Konakov, S. Menozzi and S. Molchanov. "Diffusion processes on solvable groups of upper triangular(2*2)-matrices and their approximations". [[https://link.springer.com/article/10.1134/S1064562411050036|(Russian) Doklad. Akad. Nauk. 439-5 (2011), 585-588; translation in Dokl. Math. 84-1 (2011), 527-530]].\\ * A. Bensoussan, H. Jasso-Fuentes, S. Menozzi, L. Mertz. [[https://hal.archives-ouvertes.fr/hal-00653721v1|"Asymptotic Analysis of Stochastic Variational Inequalities Modeling an Elasto-Plastic Problem with Vanishing Jumps"]]. [[https://content.iospress.com/articles/asymptotic-analysis/asy1109|Asymptotic Analysis, 80 (1-2), (2012), 171-187]].\\ * N. Frikha, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00688165v3|"Concentration bounds for Stochastic Approximations"]]. [[https://projecteuclid.org/euclid.ecp/1465263180|Electronic Communications in Probability 17 (2012), 47, 1-15]].\\ * C.Cinti, S. Menozzi, S. Polidoro. [[https://hal.archives-ouvertes.fr/hal-00681604v2|"Two sided bounds for degenerate processes with densities supported in subsets of R^N"]]. [[https://link.springer.com/article/10.1007/s11118-014-9424-7|Potential Analysis, 42-1 (2015), 39-98]].\\ * F. Delarue, S. Menozzi, E. Nualart. [[https://hal.archives-ouvertes.fr/hal-01005083v2|"The Landau Equation for Maxwellian molecules and the Brownian Motion on SO_R(N)"]]. [[https://projecteuclid.org/euclid.ejp/1465067198|Electronic Journal of Probability, 20 (2015), 92, 1-39]].\\ * M. Kelbert, V. Konakov, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01147962v1|"Weak error for continuous time Markov chains related to fractional in time P(I)DEs"]]. [[http://www.sciencedirect.com/science/article/pii/S0304414915002628|Stochastic Processes and their Applications, 126-4 (2016), 1145-1183]].\\ * L. Huang, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00947749v2|"A Parametrix Approach for some Degenerate Stable Driven SDEs"]]. [[https://projecteuclid.org/euclid.aihp/1479373254|Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 52-4 (2016), 1925-1975]]. \\ * D. Chamorro, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01098102v2|"Fractional operators with singular drift: Smoothing properties and Morrey-Campanato spaces"]]. [[http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=32&iss=4&rank=17|Revista Matemática Iberoamericana, 32-4 (2016), 1445-1499]].\\ * V. Konakov, A. Kozhina, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01169685v3|"Stability of Densities for Perturbed Diffusions and Markov Chains"]]. [[https://www.esaim-ps.org/articles/ps/abs/2017/01/ps160028/ps160028.html|ESAIM: Probability and Statistics, 21 (2017), 88-112]].\\ * V. Konakov, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01297066v3|"Weak Error for the Euler Scheme Approximation of Diffusions with Non-Smooth Coefficients"]]. [[http://projecteuclid.org/euclid.ejp/1494489631|Electronic Journal of Probability, 22 (2017), paper #46, 47p]].\\ * S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-00969037v3 |"Martingale problems for some degenerate Kolmogorov equations"]]. [[https://www.sciencedirect.com/science/article/pii/S0304414917301564|Stochastic Processes and their Applications, 128-3 (2017), 756-802]].\\ * D. Chamorro, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01383228v2|"Non Linear Singular Drifts and Fractional Operators: when Besov meets Morrey and Campanato"]].[[ https://link.springer.com/article/10.1007/s11118-017-9647-5|Potential Analysis, 49-1 (2018), 1-35]].\\ * L. Huang, S. Menozzi, E. Priola. [[https://hal.archives-ouvertes.fr/hal-01349567v2 | "L^p Estimates For Degenerate Non-Local Kolmogorov Operators"]]. [[https://www.sciencedirect.com/science/article/pii/S0021782417302039|Journal de Mathématiques Pures et Appliquées, 121 (2019), 162-215]] .\\ * I. Honoré, S. Menozzi, G. Pagès. [[https://hal.archives-ouvertes.fr/hal-01321645v3 |"Non-Asymptotic Gaussian Estimates for the Recursive Approximation of the Invariant Measure of a Diffusion"]]. [[https://www.imstat.org/journals-and-publications/annales-de-linstitut-henri-poincare/|Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 56-3 (2020), 1559–1605]].\\ * V. Konakov, S. Menozzi, S. Molchanov. [[https://hal.archives-ouvertes.fr/hal-01588913v1 | "The Brownian Motion on Aff(R) and Quasi-Local Theorems"]] [[https://www.ams.org/books/conm/ |Probabilistic methods in geometry, topology and spectral theory, 97–124, Contemp. Math., 739, Centre Rech. Math. Proc., Amer. Math. Soc., Providence, RI, 2019]].\\ * P.E. Chaudru de Raynal, S. Menozzi, E. Priola. [[https://hal.archives-ouvertes.fr/hal-02018619v1| "Schauder estimates for drifted fractional operators in the supercritical case"]]. [[https://www.sciencedirect.com/science/article/abs/pii/S0022123619304185| Journal of Functional Analysis 278 (2020), no. 8, paper #108425, 57 p]]\\ * P.E. Chaudru de Raynal, S. Menozzi, E. Priola. [[https://hal.archives-ouvertes.fr/hal-02434363v1| "Weak well-posedness of multidimensional stable driven SDEs in the critical case"]]. [[https://www.worldscientific.com/doi/10.1142/S0219493720400043| Stochastic and Dynamics 20-6 (2020), paper #2040004, 20p]]\\ * S. Menozzi, A. Pesce, Xicheng Zhang [[https://hal.archives-ouvertes.fr/hal-02864994|"Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift"]]. [[https://www.sciencedirect.com/science/article/abs/pii/S0022039620304988| Journal of Differential Equations, Vol. 272 (2021), 330-369 ]]. * N. Frikha, V. Konakov, S. Menozzi [[ https://hal.archives-ouvertes.fr/hal-02314239v1|"Well-posedness of some non-linear stable driven SDEs]]. [[https://www.aimsciences.org/journal/1078-0947 |Discrete and Continuous Dynamical Systems (Serie A) 41-2 (2021), 849-898]]. * P.E. Chaudru de Raynal, I. Honoré, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01906573v2| "Sharp Schauder Estimates for some Degenerate Kolmogorov Equations "]]. in [[https://journals.sns.it/index.php/annaliscienze/index |Annali della Scuola Normale Superiore di Pisa, classe di Scienze, Vol. 22-3 (2021), 989-1089 ]].\\ * P.E. Chaudru de Raynal, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01613679v1| "Regularization effects of a noise propagating through a chain of differential equations: an almost sharp result"]]. [[https://www.ams.org/journals/tran/earlyview/ | Transactions of the American Mathematical Society, 375-1 (2022), 1-45 ]].\\ * S. Menozzi, Xicheng Zhang. [[https://hal.archives-ouvertes.fr/hal-03088376v2| "Heat kernel of supercritical SDEs with unbounded drifts "]]. [[https://jep.centre-mersenne.org/volume/JEP_2022__9/|Journal de l'Ecole Polytechnique, Vol. 9 (2022), 537-579]]. * L. Marino, S. Menozzi, E. Priola. [[https://hal.archives-ouvertes.fr/LAMME/hal-03284221v1|"Poisson process and sharp constants in Lp and Schauder estimates for a class of degenerate Kolmogorov operators"]].[[https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/accepted|Studia Mathematica 267 (2022), no. 3, 321–346.]]\\ * P.E. Chaudru de Raynal, I. Honoré, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-01906576v1| "Strong regularization by Brownian noise propagating through a weak Hörmander structure "]] [[https://www.springer.com/journal/440?gclid=EAIaIQobChMI8pz3pNi99gIVbI9oCR1odQoNEAAYASAAEgIqO_D_BwE|Probability Theory and Related Fields,184 (2022), no. 1-2, 1–83.]]\\ * P.E. Chaudru de Raynal, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-02196382| "On Multidimensional stable-driven Stochastic Differential Equations with Besov drift "]],[[https://projecteuclid-org.ezproxy.universite-paris-saclay.fr/journals/electronic-journal-of-probability/volume-27/issue-none/On-multidimensional-stable-driven-stochastic-differential-equations-with-Besov-drift/10.1214/22-EJP864.full|Electronic Journal of Probability, 27 (2022), paper #163, 52pp.]].\\ * P. E. Chaudru de Raynal, S. Menozzi, A. Pesce, X. Zhang. [[https://hal.archives-ouvertes.fr/hal-03553730v1|"Heat kernel and gradient estimates for kinetic SDEs with low regularity coefficients"]] [[https://www.sciencedirect.com/science/article/abs/pii/S0007449723000039|Bulletin des Sciences Mathématiques, 183 (2023) paper # 103229, 48 pp]]. * L. Marino, S. Menozzi [[https://hal.archives-ouvertes.fr/hal-03281998|"Weak well-posedness for degenerate SDEs driven by Lévy processes"]] [[https://www.sciencedirect.com/science/article/abs/pii/S0304414923000807|Stochastic processes and their Applications, Vol 162, (2023), Pages 106-170]]. * B. Jourdain, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-03223426v1| "Convergence Rate of the Euler-Maruyama Scheme Applied to Diffusion Processes with L Q − L ρ Drift Coefficient and Additive Noise"]] [[https://imstat.org/journals-and-publications/annals-of-applied-probability|Annals of Applied Probability, 34(1B): 1663-1697 (2024)]]. * L. Marino, S. Menozzi, E. Priola. [[https://hal.science/hal-04117895v1|"About the regularity of degenerate non-local Kolmogorov operators under diffusive perturbations"]] in [[ https://link.springer.com/book/10.1007/978-981-97-0225-1|Kolmogorov operators and their applications (2024)]] Proceedings from the 2022 Indam conference in Cortona. * P. E. Chaudru de Raynal, J.F. Jabir, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-03676391|"Multidimensional Stable driven McKean-Vlasov SDEs with distributional interaction kernel - a regularization by noise perspective"]] [[https://link.springer.com/journal/40072|To appear in Stochastics and Partial Differential Equations (2024)]]. * D. Chamorro, S. Menozzi. [[https://hal.archives-ouvertes.fr/hal-03695479v1|"Non Linear Singular Drifts and Fractional Operators"]] [[https://link.springer.com/journal/42985|To appear in Partial Differential Equations and Applications (2024)]] =====Prépublications===== * P. E. Chaudru de Raynal, J.F. Jabir, S. Menozzi. [[https://hal.science/hal-03995199v1|"Multidimensional Stable Driven McKean-Vlasov SDEs with Distributional Interaction Kernel: Critical Thresholds and Related Models"]] (2023). * V. Konakov, S. Menozzi.[[https://hal.science/hal-04330201|"Limit Theorems for Random Walks in the Hyperbolic Space"]] (2023). * M. Fitoussi, B. Jourdain, S. Menozzi. [[https://hal.sorbonne-universite.fr/CERMICS/hal-04571879v1|Weak well-posedness and weak discretization error for stable-driven SDEs with Lebesgue drift]] (2024) * J.F. Jabir, Z. Hao, S. Menozzi, M. Röckner, X. Zhang. [[https://cnrs.hal.science/LAMME/hal-04575065v1|Propagation of Chaos for Moderately Interacting Particle Systems Related to Singular Kinetic McKean-Vlasov SDEs]] (2024) * M. Fitoussi, S. Menozzi. [[https://hal.science/hal-04733240v1|Weak error on the densities for the Euler scheme of stable additive SDEs with Hölder drift ]] (2024) * G. Lucertini, S. Menozzi, S. Pagliarani.[[https://arxiv.org/abs/2410.13432| Strong regularization by noise for a class of kinetic SDEs driven by symmetric α-stable processes]] (2024) =====Evénements ===== * [[https://gp60.sciencesconf.org/|Conference of Numerical Probability in honour of Gilles Pagès' 60th birthday]]\\ * [[https://www.koa2022.unimore.it/|Kolmogorov operators and Applications]] ===== ORCiD ===== [[https://orcid.org/0000-0001-5069-6067|orcid.org/0000-0001-5069-6067]] {{:members:lemarie:orcid_16x16.png?50|orcid.org/0000-0001-5069-6067}} =====Enseignement 2018-2020:===== * Calcul Stochastique et Applications à la finance au: [[https://www.universite-paris-saclay.fr/en/formation/master/mathematics-and-applications/m2-quantitative-finance http://www.math-evry.cnrs.fr/departement/doku.php?id=formation:master:m2if/|Master 2 d'Ingénierie financière, Université d'Evry]]\\ * Espaces de Fonctions (Licence 3 de Mathématiques)\\ * Mathématiques pour la Physique (Licence 2 et 3 de Physique)\\ =====Enseignement 2020-2021:===== * Finance numérique pour le M2 Quantitative Finance: [[https://www.universite-paris-saclay.fr/en/formation/master/mathematics-and-applications/m2-quantitative-finance|Master 2 d'Ingénierie financière, Université d'Evry, Paris-Saclay (Site UPSAY)]][[ http://www.math-evry.cnrs.fr/departement/doku.php?id=formation:master:m2if/| Master 2 d'Ingénierie financière, Université d'Evry (site d'Evry)]]\\ * Mathématiques pour la Physique (Licence 2 et 3 de Physique) * Optimisation Numérique au Master 1 de Mathématiques. * Equations de Navier Stokes [[https://www.universite-paris-saclay.fr/formation/master/mecanique/m2-mathematique-et-mecanique-fondamentale|Master 2 de Mathématique et Mécanique fondamentale]] =====Enseignement 2021-2022:===== * Mathématiques pour la Physique (Licence 2 et 3 de Physique)\\ * Algèbre et Géométrie, Licence 3 de Mathématiques.\\ * Optimisation Numérique et Simulation probabiliste, Master 1 de Mathématiques.\\ * EDP et Méthodes hilbertiennes, Master 1 de Mathématiques.\\ * Equations de Navier Stokes [[https://www.universite-paris-saclay.fr/formation/master/mecanique/m2-mathematique-et-mecanique-fondamentale|Master 2 de Mathématique et Mécanique fondamentale]] =====Responsabilités pédagogiques 2020-2022:===== * Responsable UEVE du M2 de Finance Quantitative[[ http://www.math-evry.cnrs.fr/departement/doku.php?id=formation:master:m2if/| Master 2 d'Ingénierie financière, Université d'Evry (site d'Evry)]]