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