Large deviation principle for slow-fast systems with infinite-dimensional mixed fractional Brownian motion

TL;DR

This paper establishes a large deviation principle for slow-fast systems influenced by infinite-dimensional mixed fractional Brownian motion, using weak convergence methods and relaxing previous boundedness assumptions.

Contribution

It introduces a novel approach to analyze large deviations in infinite-dimensional systems with fractional noise, extending existing theories and establishing moderate deviation principles.

Findings

Proved large deviation principle for the systems.

Established moderate deviation principle.

Dropped boundedness assumptions on coefficients.

Abstract

This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method which is based on the variational representation formula for infinite-dimensional mixed fractional Brownian motion. To obtain the weak convergence of the controlled systems, we apply the Khasminskii's averaging principle and the time discretization technique. In addition, we drop the boundedness assumption of the drift coefficients of the slow components and the diffusion coefficients of the fast components.Based on the proof of the large deviation principle, we also establish the moderate deviation principle for the slow-fast systems.