Asymptotically almost periodic solutions of stochastic functional differential equations

In this paper, we investigate a class of stochastic functional differential equations of the form $\mathit{dx}(t)=(\mathit{Ax}(t)+F(t\text{,}x(t)\text{,}{x}_t))\mathit{dt}+G(t\text{,}x(t)\text{,}{x}_t)°\mathit{dW}(t)\text{.}$ Our main results concern the existence and exponential stability of quadratic‐mean asymptotically almost periodic mild solutions. An example is given to illustrate our results.