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