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