A Strong Limit Theorem for Two-Time-Scale Fucntional Stochastic Differential Equations

TL;DR

This paper establishes a strong limit theorem for two-time-scale functional stochastic differential equations with infinite-dimensional phase spaces, extending averaging principles to complex stochastic systems.

Contribution

It develops ergodicity for the fast component and proves a strong averaging limit theorem for the slow component in infinite-dimensional settings.

Findings

Proves ergodicity of the fast component.

Establishes a strong averaging limit theorem.

Extends averaging principles to infinite-dimensional systems.

Abstract

This paper focuses on a class of two-time-scale functional stochastic differential equations, where the phase space of the segment processes is infinite-dimensional. It develops ergodicity of the fast component and obtains a strong limit theorem for the averaging principle in the spirit of Khasminskii's averaging approach for the slow component.