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Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations. (English) Zbl 1185.35345
The authors investigate the stochastic evolution equation $dX(t) = A X(t) dt +F(t,X(t))dt +G(t,(t))dW(t)$ driven by a Wiener process $W$ and taking values in a separable Hilbert space. They provide sufficient conditions on the coefficients for the existence of a quadratic-mean almost periodic solution, one of them being the quadratic-mean almost periodicity of $F$ and $G$.

35R60PDEs with randomness, stochastic PDE
35B15Almost and pseudo-almost periodic solutions of PDE
60H10Stochastic ordinary differential equations
60H15Stochastic partial differential equations
35B30Dependence of solutions of PDE on initial and boundary data, parameters
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