Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations

TL;DR

This paper introduces a nonlinear forward Feynman-Kac equation that represents solutions to non-conservative semilinear parabolic PDEs, establishing existence, uniqueness, and a particle system approach for solutions.

Contribution

It presents a novel forward Feynman-Kac representation for non-conservative PDEs and demonstrates how to approximate solutions using a weighted particle system.

Findings

Existence and uniqueness of the proposed equation are proven.

A weighted particle system approach is developed for solution approximation.

The method provides a new probabilistic representation for non-conservative PDEs.

Abstract

We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.