Large deviation principle for slow-fast system with mixed fractional Brownian motion

TL;DR

This paper establishes a large deviation principle for a slow-fast stochastic system driven by mixed fractional Brownian motion, using variational methods and weak convergence techniques.

Contribution

It introduces a novel approach combining weak convergence and Khasminskii's averaging to analyze large deviations in mixed fractional Brownian systems.

Findings

Large deviation principle proven for the slow component

Method applicable to systems with mixed fractional Brownian motion

Framework extends existing large deviation results to new stochastic models

Abstract

This work focuses on a slow-fast system perturbed by mixed fractional Brownian motion with Hurst parameter $H\in(1/2,1)$. The integral with respect to fractional Brownian motion is the generalized Riemann-Stieltjes integral and the integral with respect to Brownian motion is the standard It\^o integral. Our approach is based on the variational framework and the weak convergence criteria for mixed fractional Brownian motion. By combining the weak convergence method and Khasminskii's averaging principle, we show a large deviation principle for the slow component.