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Zbl 1185.35345
Bezandry, Paul H.; Diagana, Toka
Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations. (English)
[J] Electron. J. Differ. Equ. 2009, Paper No. 111, 14 p., electronic only (2009). ISSN 1072-6691/e

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 $G$.
[Michael Scheutzow (Berlin)]

MSC 2000:: *35R60 PDE with randomness
35B15 Almost periodic solutions of PDE
60H10 Stochastic ordinary differential equations
60H15 Stochastic partial differential equations
35B30 Dependence of solutions of PDE on initial and boundary data

Keywords: stochastic differential equation; stochastic partial differential equation; stochastic processes; quadratic mean almost periodicity; Wiener process

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