Existence of almost automorphic mild solutions to non-autonomous neutral stochastic differential equations

In this paper, we consider the existence and uniqueness of square-mean and weighted pseudo almost automorphic mild solutions to a class of nonautonomous stochastic neutral differential equations with infinite delay in real separable Hilbert spaces. A new set of sufficient conditions are established for obtaining the required result. To prove the main result, we use Banach contraction principle together with evolution family of operators. Some known results are generalized and improved. An application to the stochastic nonlinear heat equation with infinite delay is provided to illustrate the obtained theory.