May 2024 Comparison principle for stochastic heat equations driven by α-stable white noises
Yongjin Wang, Chengxin Yan, Xiaowen Zhou
Author Affiliations +
Bernoulli 30(2): 1375-1400 (May 2024). DOI: 10.3150/23-BEJ1635

Abstract

For a class of non-linear stochastic heat equations driven by α-stable white noises for α(1,2) with Lipschitz coefficients, we prove the existence and pathwise uniqueness of Lp-valued càdlàg solution to such an equation for p(α,2] by considering a sequence of approximating stochastic heat equations driven by truncated α-stable white noises obtained by removing the big jumps from the original α-stable white noise. If the α-stable white noise is spectrally one-sided, under additional monotonicity assumption on noise coefficients, we further prove a comparison theorem on the L2-valued càdlàg solutions to such an equation. As a consequence, the non-negativity of the L2-valued càdlàg solution is established for the above stochastic heat equation with non-negative initial function.

Funding Statement

The first and second authors are supported by the National Natural Science Foundation of China (NSFC) (Nos. 11631004, 71532001). The third author is supported by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2021-04100).

Acknowledgments

The authors would like to thank Prof. Bin Xie for providing their article as our important reference. They also thank editors and anonymous referees for careful reading of the manuscript and for providing a number of useful comments and suggestions that have greatly improved the presentation of the paper.

Citation

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Yongjin Wang. Chengxin Yan. Xiaowen Zhou. "Comparison principle for stochastic heat equations driven by α-stable white noises." Bernoulli 30 (2) 1375 - 1400, May 2024. https://doi.org/10.3150/23-BEJ1635

Information

Received: 1 November 2022; Published: May 2024
First available in Project Euclid: 31 January 2024

MathSciNet: MR4699556
Digital Object Identifier: 10.3150/23-BEJ1635

Keywords: Comparison principle , non-negative solutions , Stochastic heat equations , truncated α-stable white noises , α-stable white noises

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Vol.30 • No. 2 • May 2024
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