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