The Non-Archimedean Stochastic Heat Equation driven by Gaussian Noise

TL;DR

This paper introduces a new class of non-Archimedean stochastic heat equations driven by Gaussian noise, establishing their existence and uniqueness of solutions in a novel mathematical setting.

Contribution

It develops the theory of non-Archimedean stochastic pseudodifferential equations, extending classical stochastic heat equation results to a non-Archimedean context.

Findings

Existence of mild random field solutions

Uniqueness of solutions for the equations

Extension of stochastic heat equation theory to non-Archimedean fields

Abstract

We introduce and study a new class of non-Archimedean stochastic pseudodifferential equations. These equations are the non-Archimedean counterparts of the classical stochastic heat equations. We show the existence and uniqueness of mild random field solutions for these equations.