Parabolic Equations and Markov Processes Over p-adic Fields

TL;DR

This paper constructs a fundamental solution for p-adic parabolic equations, linking it to the transition density of a corresponding p-adic Markov process, thus advancing the understanding of p-adic stochastic processes.

Contribution

It introduces a method to explicitly construct fundamental solutions for p-adic parabolic equations and connects these solutions to p-adic Markov processes.

Findings

Fundamental solution explicitly constructed

Transition density identified as fundamental solution

Advances understanding of p-adic stochastic processes

Abstract

We construct and study a fundamental solution of Cauchy's problem for p-adic parabolic equations of a certain the type. The fundamental solution is the transition density of a p-adic Markov process.