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

TL;DR

This paper develops a probabilistic particle algorithm to solve nonconservative semilinear parabolic PDEs using a forward Feynman-Kac representation, demonstrating its effectiveness through numerical experiments.

Contribution

It introduces a novel particle algorithm for semilinear PDEs based on forward Feynman-Kac formulas, expanding computational tools for nonconservative equations.

Findings

Algorithm shows high efficiency in numerical tests

Effective for nonconservative semilinear PDEs

Potential for broad applications in stochastic modeling

Abstract

The paper is devoted to the construction of a probabilistic particle algorithm. This is related to nonlin-ear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.