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