Large Deviations for Stochastic Integrodifferential Equations of the Ito type with Multiple Randomness

Abstract

A Freidlin-Wentzell type large deviation principle is derived for a class of Itˆo type stochastic integrodifferential equations driven by a finite number of multiplicative noises of the Gaussian type. As a consequence of Varadhan’s lemma and Bryc’s converse to Varadhan’s lemma, the large deviation principle is equivalent to the Laplace principle in a Polish space. The Laplace principle is therefore proved here using the weak convergence approach.