Generalized solutions of differential-operator equations with singular white noise

Abstract

In various distribution spaces, we study the Cauchy problem for the equation u′(t) = Au(t)+BW(t), t ≥ 0, with a singular white noise W and an operator A generating various regularized semigroups in a Hilbert space. Depending on the properties of the operator A, we construct solutions generalized separately and jointly with respect to the time, random, and "space" variables. © 2013 Pleiades Publishing, Ltd.