Stochastic differential equations are the problem of phenomena in the natural science. a class of mathematical models

which are established to solve Square-mean asymptotically almost automorphic mild solutions of stochastic differential equations have a wider application range than square-mean almost automorphic mild solutions. The definition of square-mean asymptotically almost automorphic stochastic processes and some basic properties are introduced. The existence and uniqueness of square-mean asymptotically almost automorphic solutions of non-auton- omous stochastic differential equations with delay in a real separable Hilbert space are studied

by using the Banach fixed point theorem

the exponential stability of convolution family and the related properties of the square-mean as- ymptotically almost automorphic stochastic processes.