Pseudo Almost Automorphic Mild Solution of Nonautonomous Stochastic Functional Integro-differential Equations

Abstract

In this paper, we propose a new class of stochastic process called $(\mu,\nu)$-pseudo almost automorphic in $p$-mean, which generalize in a natural fashion the concept of square-mean almost automorphy and its various extensions. As application, we establish the existence, uniqueness of $(\mu,\nu)$-pseudo almost automorphic in $p$-distribution mild solution to nonautonomous stochastic functional integro-differential equations. Finally, an example is given to illustrate the significance of the main findings.