Remotely almost periodicity for SDEs under the framework of evolution system

Abstract

In this paper, we introduce the concepts of [Formula: see text]-remotely almost periodic processes and remotely almost periodicity in distribution. Under the framework of evolution system, we establish [Formula: see text]-remotely almost periodicity and remotely almost periodicity in distribution for solutions to stochastic differential equations (SDEs) [Formula: see text] in infinite dimensions. Our main results extend some earlier results about the above SDEs in the cases of [Formula: see text] and almost periodic coefficients, without assuming that [Formula: see text] is periodic as in a classical result by Da Prato and Tudor. The main difficulties lie in the loss of compactness for [Formula: see text]-remotely almost periodic processes and the delicate analysis caused by evolution system. Moreover, our abstract results can be applied to some stochastic parabolic partial differential equations.