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