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