Abstract:Some concepts and properties of square-mean asymptotically automorphic function and stochastic process are introduced. Underlying some assumptions

C0semigroup and the Banach fixed point theorem and Cauchy Schwarz inequality are used to discuss the existence and uniqueness of Square-mean asymptotically almost automorphic mild solutions

in a real separable Hilbert space

for a class of abstract semilinear stochastic integro differential evolution equations.