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 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.