On generalized solutions to stochastic systems

Abstract

We consider the Cauchy problem for systems of differential equations with white noise type random perturbations. Generalized solutions with respect to spatial variable x of the problem in the Itô statement are obtained in spaces Ψ′ depending on a type of the system. Generalized solutions with respect to t and x of the problem in the differential statement are obtained in spaces D′ (Ψ′).