Retarded Neutral Stochastic Equations Driven by Multiplicative Fractional Brownian Motion

Abstract

In this article, we develop an existence and uniqueness theory of pathwise mild solutions for a class of stochastic neutral partial functional differential equations that are driven by an infinite-dimensional multiplicative fractional noise. Our existence and uniqueness result is divided into two parts: first we establish the existence and uniqueness of a local solution, which proof rests upon the Banach fixed point theorem; then the existence of a unique global solution is based on certain regularity properties of the local solution as well as a suitable way of extending the local solution to the entire interval in finitely many steps.