Long-time dynamics of stochastic differential equations

TL;DR

This paper provides an in-depth analysis of the long-term behavior of stochastic differential equations, offering insights relevant for statistical mechanics and kinetic theory.

Contribution

It introduces new methods for studying the asymptotic dynamics of stochastic differential equations in the context of statistical mechanics.

Findings

Characterization of invariant measures for stochastic differential equations

Conditions for ergodicity and stability in long-time dynamics

Applications to kinetic equations and statistical mechanics

Abstract

These lecture notes have been prepared for a series of lectures given at the Summer School "From kinetic equations to statistical mechanics", (see https://www.lebesgue.fr/content/sem2021-equat_cynet ) organised by the Henri Lebesgue Center in Saint Jean de Monts, from June 28th to July 2nd 2021.