The applications of the theories of square-mean almost automorphic type functions have attracted more and more attention by mathematics researchers

square-mean asymptotically almost automorphic solutions of this class of differential equations have a wider range of applications than square-mean almost automorphic solutions.Square-mean asymptotically almost automorphic mild solutions to a class of semi-linear stochastic differential equations are investigated. The existence and uniqueness of square-mean asymptotically almost automorphic mild solutions for this kind of equation are discussed by using the principle of Banach compressed image

combining with the definition and properties of square-mean asymptotically almost automorphic stochastic processes， Cauchy-Schwarz inequality

Lipschtiz conditions and Ito integrals isometry.