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 \(G\).


35R60 PDEs with randomness, stochastic partial differential equations
35B15 Almost and pseudo-almost periodic solutions to PDEs
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
Full Text: EuDML Link