Stochastic solutions and singular partial differential equations

TL;DR

This paper extends stochastic solution techniques to partial differential equations influenced by distribution-valued noises, offering a novel approach for solving such complex equations.

Contribution

It introduces the use of stochastic solutions for PDEs driven by distribution-valued noises, expanding the applicability of stochastic methods.

Findings

Demonstrates the feasibility of stochastic solutions for new classes of PDEs.

Provides a framework for solving PDEs with distribution-valued noise.

Shows potential for applications in complex stochastic modeling.

Abstract

The technique of stochastic solutions, previously used for deterministic equations, is here proposed as a solution method for partial differential equations driven by distribution-valued noises.