Solutions of Hyperbolic Stochastic PDEs on Bounded and Unbounded Domains

Abstract We treat several classes of hyperbolic stochastic partial differential equations in the framework white noise analysis, combined with Wiener–Itô chaos expansions and Fourier integral operator methods. The input data, boundary conditions coefficients operators are assumed to be generalized processes that have both temporal spatial dependence. prove under consideration unique solutions appropriate Sobolev–Kondratiev or weighted-Sobolev–Kondratiev spaces. Moreover, an explicit form is obtained, useful for calculating expectations, variances higher order moments solution.