Towards a Quantitative Averaging Principle for Stochastic Differential Equations

Abstract: This work explores the use of a forward-backward martingale method together with a decoupling argument and entropic estimates between the conditional and averaged measures to prove a strong averaging principle for stochastic differential equations with order of convergence 1/2. We obtain explicit expressions for all the constants involved. At the price of some extra assumptions on the time marginals and an exponential bound in time, we loosen the usual boundedness and Lipschitz assumptions. We conclude with an application of our result to Temperature-Accelerated Molecular Dynamics.