Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions

Abstract

In this paper, we study small-noise asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter H∈(1/2,1) and magnitude ϵH. By building up a variational framework and two weak convergence criteria in the factional Brownian motion setting, we establish the large and moderate deviation principles for these types of equations. Besides, we also obtain the central limit theorem, in which the limit process solves a linear equation involving the Lions derivative of the drift coefficient.