Large and moderate deviation principles for path-distribution-dependent stochastic differential equations

Abstract

In this paper, by weak convergence method, large and moderate deviation principles are established for path-distribution-dependent stochastic differential equations. To prove large deviation principle, both of the drift and diffusion coefficients are required to be Lipschitz continuous in the space variable as well as the distribution term, uniformly with respect to the time parameter $ t $. In further, to establish the moderate deviation principle, the drift coefficient is assumed to be Frechet differentiable with Lipschitz continuous derivative in the space variable.