Nonlinear stochastic wave equation with Colombeau generalized stochastic processes

Abstract

Colombeau generalized stochastic processes are introduced in order to solve nonlinear wave and Klein-Gordon equations with stochastic processes. Particular cases include one- and three-dimensional wave and Klein-Gordon equations with Lipschitz and cubic nonlinearities. In all cases, considered as Colombeau generalized stochastic processes, solutions are obtained and proved to be unique. The normalizations of the initial data and stochastic processes appear to be the crucial points for the existence of solutions to the above equations.