On the Transfer of Generalized Functions by an Evolution Flow

Abstract

We investigate properties of a solution of a stochastic differential equation with interaction and their dependence on a space variable. It is shown that $x(u, t) − u$ belongs to $S$ under certain conditions imposed on the coefficients, and, furthermore, it depends continuously on the initial measure as an element of S. We also study the problem of the existence of a solution of the equation governed by a generalized function.