Burgers equation Cox processes Markov process Backward stochastic differential equation Analyse stochastique EDP Small ball estimate Conservation laws Feller processes Diffusion-approximation White noise dispersion Multilevel splitting Invariant measure Stochastic optimal control Mesures invariantes Coupling Existence and uniqueness Stochastic differential equation Forward-backward stochastic differential equation Ergodicité Kinetic formulation Blow-up Comparison theorem Lévy processes Nonlinear Schrödinger equation Generalized random fields Central limit theorem Time-inconsistency Propagation of chaos Second Wiener chaos Piecewise deterministic Markov process Fractional Brownian motion Rare event simulation Équations différentielles stochastiques Ergodicity Dual representation Backward error analysis Explosion times Long-time behavior Ergodic control Quadratic growth Feynman-Kac formula Lévy process Solitary waves Stochastic partial differential equations Analysis of PDEs mathAP Kac-Rice formula Kinetic equation Stochastic linear-quadratic control Backward stochastic differential equations Importance sampling Rare event 2-Wasserstein distance 60H10 Equations aux dérivées partielles stochastiques Wasserstein distance Kinetic equations Edgeworth expansion Limit theorems Perturbed test functions Invariant measures Differential equations FOS Mathematics Probability mathPR Croissance quadratique Stochastic partial differential equation Random walk Brownian motion Stochastic differential equations BMO martingale Exponential mixing Concentration inequalities Uniqueness Diffusion limit Adjoint process Asymptotic distributions Interacting particle systems White noise Particle filter Convex optimization Comportement en temps long Approximation diffusion Probability Probabilités Coupling method Stochastic processes Champs aléatoires Particle filtering Point processes Processus de Lévy Asymptotic distribution Kinetic stochastic equation Kolmogorov equation Malliavin calculus Fomin differentiability G-Brownian motion BSDE Champ moyen Processus de Markov Piecewise Deterministic Markov Process