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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 )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.

60H10Stochastic ordinary differential equations
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