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

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 Itô 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.