Nesting Monte Carlo for high-dimensional Non Linear PDEs

TL;DR

This paper introduces a nesting Monte Carlo method for efficiently solving high-dimensional semi-linear PDEs, with proven convergence and demonstrated effectiveness across various non-linearities.

Contribution

The paper develops a novel nesting Monte Carlo approach with theoretical convergence guarantees for high-dimensional semi-linear PDEs.

Findings

Proven convergence of the method.

Effective in high dimensions for different non-linearities.

Demonstrates efficiency through numerical results.

Abstract

A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Convergence of the method is proved and its convergence rate studied. Results in high dimension for different kind of non-linearities show its efficiency.