Weak Averaging of Semilinear Stochastic Differential Equations with Almost Periodic Coefficients

TL;DR

This paper proves an averaging principle for semilinear stochastic differential equations with almost periodic coefficients, demonstrating convergence in distribution to an averaged equation, extending previous theoretical results.

Contribution

It introduces a new averaging result for stochastic equations with almost periodic coefficients, correcting earlier errors and broadening the applicability of such methods.

Findings

Convergence in distribution to the averaged solution

Applicable to equations with almost periodic coefficients

Extends previous averaging results in stochastic analysis

Abstract

An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged equation is obtained in distribution, as in previous works by Khasminskii and Vrko{\v c}.This version corrects two minor errors from our paper published in J. Math. Anal. Appl. 427(1):336--364, 2015.