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

Abstract

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.

Keywords

• Stochastic differential equations
• Square-mean almost automorphic processes
• Mild solutions