Towards a Quantitative Averaging Principle for Stochastic Differential Equations

TL;DR

This paper develops a quantitative averaging principle for stochastic differential equations using advanced probabilistic methods, providing explicit constants and relaxing traditional assumptions, with applications to molecular dynamics.

Contribution

It introduces a strong averaging principle with explicit constants for SDEs, relaxing boundedness and Lipschitz conditions through new probabilistic techniques.

Findings

Proves a strong averaging principle with convergence order 1/2.

Provides explicit constants for the averaging estimates.

Applies the results to Temperature-Accelerated Molecular Dynamics.

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.