Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space

Abstract

This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results, we use the Banach contraction mapping principle and the techniques of fractional powers of an operator. Mathematics Subject Classification (2000) 34K14, 60H10, 35B15, 34F05.

Square-mean asymptotically almost automorphic mild solutions to non-autonomous stochastic differential equations

“…In this section, we introduce some basic definitions, notations, lemmas and technical results which will be used in the sequel. For more details on this section, we refer the reader to [7,13].…”

“…Recently, the existence of almost periodic, almost automorphic and pseudo almost automorphic solutions to some stochastic differential equations have been considered in many publications such as [4,5,7,8,10,18] and references therein. In a very recent paper [8], the authors introduced a new concept of S 2 -almost automorphy for stochastic processes including a composition theorem.…”

Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations

“…Recently, the existence of almost automorphic and pseudo almost automorphic solutions to some stochastic differential equations has been considered in many publications such as [17][18][19][20][21][22][23][24][25][26][27] and the references therein. In a very recent paper [28], the authors introduced a new notation of square-mean asymptotically almost automorphic stochastic processes including a composition theorem.…”