Averaging principle for slow-fast stochastic differential equations with time dependent locally Lipschitz coefficients

TL;DR

This paper establishes an averaging principle for slow-fast stochastic differential equations with time-dependent coefficients, proving strong convergence of the slow component to an averaged solution using discretization and truncation techniques.

Contribution

It extends the averaging principle to stochastic differential equations with time-dependent locally Lipschitz coefficients, providing a rigorous convergence proof.

Findings

Strong convergence of the slow component to the averaged equation

Applicability to equations with time-dependent coefficients

Use of discretization and truncation methods for proof

Abstract

This paper is devoted to studying the averaging principle for stochastic differential equations with slow and fast time-scales, where the drift coefficients satisfy local Lipschitz conditions with respect to the slow and fast variables, and the coefficients in the slow equation depend on time $t$ and $\omega$. Making use of the techniques of time discretization and truncation, we prove that the slow component strongly converges to the solution of the corresponding averaged equation.