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Asymptotically almost periodic solutions of stochastic functional differential equations. (English) Zbl 1230.60058
Summary: We investigate a class of stochastic functional differential equations of the form \[ dx(t)=(Ax(t)+F(t,x(t),x_{t}))dt+G(t,x(t),x_{t})\circ dW(t). \] 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.

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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