Stochastic heat equations driven by space-time $G$-white noise under sublinear expectation

TL;DR

This paper investigates the stochastic heat equation driven by space-time $G$-white noise under sublinear expectations, establishing existence, uniqueness, and moment estimates for solutions, and generalizing stochastic Fubini theorem.

Contribution

It introduces a framework for analyzing stochastic heat equations with $G$-white noise under sublinear expectations, proving key properties and extending existing theorems.

Findings

Existence and uniqueness of mild solutions are established.

Mild solutions are also shown to be weak solutions.

Moment estimates for solutions are derived.

Abstract

In this paper, we study the stochastic heat equation driven by a multiplicative space-time $G$-white noise within the framework of sublinear expectations. The existence and uniqueness of the mild solution are proved. By generalizing the stochastic Fubini theorem under sublinear expectations, we demonstrate that the mild solution also qualifies as a weak solution. Additionally, we derive moment estimates for the solutions.