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