On almost periodic mild solutions for stochastic functional differential equations

In this paper, a class of stochastic functional differential equations given by dx(t) = (Ax(t) + F(t, x(t), x(t)))dt + G(t, x(t), x(t)) o d omega(t), t is an element of [0, T], x(t) = phi(t) for t is an element of [-sigma, 0], is investigated. Under some suitable assumptions, the existence and stability of quadratic-mean almost periodic mild solutions for the equations are discussed by means of semigroups of operators and fixed point method. Moreover, an example is given to illustrate our results. Crown Copyright (C) 2011 Published by Elsevier Ltd. All rights reserved.