Non-local Operators, Non-Archimedean Parabolic-type Equations with Variable Coefficients and Markov Processes

TL;DR

This paper introduces a new class of p-adic parabolic pseudo differential equations with variable coefficients, establishes their well-posedness, and links their solutions to Markov processes, with applications to complex system models.

Contribution

It presents the first analysis of p-adic parabolic equations with variable coefficients and connects solutions to Markov processes, expanding mathematical tools for complex systems.

Findings

Existence and uniqueness of solutions established.

Fundamental solutions linked to Markov processes.

Applications to modeling complex systems.

Abstract

In this article, we introduce a new class of parabolic-type pseudo differential equations with variable coefficients over the p-adics. We establish the existence and uniqueness of solutions for the Cauchy problem associated with these equations. The fundamental solutions of these equations are connected with Markov processes. Some of these equations are related to new models of complex systems.