Nonhomogeneous first-order linear Malliavin type differential equation

Abstract

© Springer Basel 2013. All rights reserved. In this paper we solve a nonhomogeneous first-order linear equation involving the Malliavin derivative operator with stochastic coefficients by use of the chaos expansion method. We prove existence and uniqueness of a solution in a certain weighted space of generalized stochastic distributions and represent the obtained solution in the Wiener-Itô chaos expansion form.