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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 $$\align dx(t) &= (Ax(t)+ F(t, x(t), xt))\,dt+ G(t,x(t), x_t)\circ d\omega(t),\quad t\in [0,T],\\ x(t) &= \varphi(t)\quad\text{for }t\in [-\sigma,0],\endalign$$ 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.

34K50Stochastic functional-differential equations
34K14Almost and pseudo-periodic solutions of functional differential equations
34K20Stability theory of functional-differential equations
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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