High Order Heat-type Equations and Random Walks on the Complex Plane

TL;DR

This paper introduces a probabilistic method to solve high order heat-type equations using the scaling limits of complex plane random walks, providing a novel connection between stochastic processes and differential equations.

Contribution

It presents a new probabilistic construction for high order heat equations based on complex plane random walks, extending existing methods.

Findings

Established a link between complex random walks and high order heat equations.

Derived solutions as scaling limits of complex random walks.

Demonstrated the effectiveness of the probabilistic approach for these equations.

Abstract

A probabilistic construction for the solution of a general class of high order heat-type equations is constructed in terms of the scaling limit of random walks in the complex plane.