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