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

Xiaojun Ji; Shige Peng

doi:10.1214/25-aap2211

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arXiv · 2407.17806

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

Xiaojun Ji·Shige Peng

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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.

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BibTeX RIS

Xiaojun Ji, Shige Peng. 2024-07-25. Stochastic heat equations driven by space-time $G$-white noise under sublinear expectation. https://doi.org/10.1214/25-aap2211

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