Bezandry, Paul H.; Diagana, Toka Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations. (English) Zbl 1185.35345 Electron. J. Differ. Equ. 2009, Paper No. 111, 14 p. (2009). 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 \(G\). Reviewer: Michael Scheutzow (Berlin) Cited in 13 Documents MSC: 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 Keywords:stochastic differential equation; stochastic partial differential equation; stochastic processes; quadratic mean almost periodicity; Wiener process PDFBibTeX XMLCite \textit{P. H. Bezandry} and \textit{T. Diagana}, Electron. J. Differ. Equ. 2009, Paper No. 111, 14 p. (2009; Zbl 1185.35345) Full Text: EuDML Link