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