Large deviation principle for multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motions

Abstract

In this paper, we are concerned with multi-scale distribution-dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index \(H>\frac{1}{2}\)) and standard Brownian motion, simultaneously. Our aim is to establish a large deviation principle for the multi-scale distribution-dependent stochastic differential equations. This is done via the weak convergence approach and our proof is based heavily on the fractional calculus.