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