Stochastic solutions of nonlinear pde's: McKean versus superprocesses

TL;DR

This paper compares two stochastic methods, McKean and superprocesses, for solving nonlinear PDEs, highlighting their respective advantages and limitations, and emphasizing their potential for parallel computation.

Contribution

It provides a comparative analysis of McKean and superprocess approaches, clarifying their strengths, limitations, and applicability to nonlinear PDEs.

Findings

McKean and superprocess methods have distinct advantages for nonlinear PDEs.

Superprocesses are particularly suited for parallel computation due to their local non-grid nature.

The paper discusses the limitations of both stochastic approaches.

Abstract

Stochastic solutions not only provide new rigorous results for nonlinear pde's but also, through its local non-grid nature, are a natural tool for parallel computation. There are two methods to construct stochastic solutions: the McKean method and superprocesses. Here a comparison is made of these two approaches and their strenghts and limitations are discussed.