On Stochastic generalized functions

TL;DR

This paper introduces a new algebra of stochastic generalized functions that extends stochastic distributions, and applies it to prove existence and uniqueness of solutions for stochastic Cauchy problems with singularities.

Contribution

The paper develops a novel algebraic framework for stochastic generalized functions, enabling analysis of stochastic equations with singularities.

Findings

Established a new algebraic structure for stochastic generalized functions.

Proved existence and uniqueness of solutions for stochastic Cauchy problems with singularities.

Extended the space of stochastic distributions to include the new algebra.

Abstract

We introduced a new algebra of stochastic generalized functions which contains to the space of stochastic distributions G, [25]. As an application, we prove existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.