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On almost periodic mild solutions for stochastic functional differential equations. (English) Zbl 1244.34100
Summary: The class of stochastic functional differential equations given by \[ \begin{aligned} dx(t) &= (Ax(t)+ F(t, x(t), xt))\,dt+ G(t,x(t), x_t)\circ d\omega(t),\quad t\in [0,T],\\ x(t) &= \varphi(t)\quad\text{for }t\in [-\sigma,0],\end{aligned} \] is investigated. Under some suitable assumptions, the existence and stability of quadraticmean 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.

MSC:
34K50 Stochastic functional-differential equations
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
47N20 Applications of operator theory to differential and integral equations
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