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),xt))dt+G(t,x(t),xt)∘dω(t),t∈[0,T],x(t)=φ(t)fort∈[−σ,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.