Taibleson Operators, p-adic Parabolic Equations and Ultrametric Diffusion

TL;DR

This paper introduces a multimensional p-adic heat equation and demonstrates that its fundamental solution serves as the transition density for a corresponding Markov process, linking p-adic analysis with stochastic processes.

Contribution

It extends the p-adic heat equation to multiple dimensions and establishes its fundamental solution as a Markov process transition density, advancing p-adic diffusion theory.

Findings

Fundamental solution is the transition density of a Markov process

Extension of p-adic heat equation to multiple dimensions

Connection between p-adic PDEs and stochastic processes

Abstract

We give a multimensional version of the p-adic heat equation, and show that its fundamental solution is the transition density of a Markov process.