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