LARGE DEVIATIONS FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS

Abstract

In this paper, we study the large deviations for a class of stochastic differential equations with deviating arguments. The randomness is assumed to be Gaussian, and both additive and multiplicative noise types are considered. We adopt the contraction principle argument and weak convergence approach to establish the Freidlin-Wentzell type large deviation principle for the additive and multiplicative noise cases respectively.