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