PreprintCC BY 4.0arXiv
Central Limit Theorem for Stochastic Nonlinear Heat Equation with Pure-Jump Lévy White Noise
Abstract
In this article, we consider the stochastic nonlinear heat equation driven by Lévy space-time white noise in dimension one. For the spatial average of the solution, we prove quantitative and functional central limit theorems under m1+m2p<∞ for some p∈(1,3/2). These results extend the Gaussian fluctuation theory for the parabolic Anderson model to the nonlinear setting. The main new feature is a minimum-type term in the second Malliavin derivative estimate caused by the nonlinear coefficient.
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BibTeX
@misc{gall2026central,
title = {{Central Limit Theorem for Stochastic Nonlinear Heat Equation with Pure-Jump Lévy White Noise}},
author = {Matis Le Gall and Jinxin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29023},
eprint = {2609.29023},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29023},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Central Limit Theorem for Stochastic Nonlinear Heat Equation with Pure-Jump Lévy White Noise
AU - Matis Le Gall
AU - Jinxin Wang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29023
UR - https://arxiv.org/abs/2609.29023
AB - In this article, we consider the stochastic nonlinear heat equation driven by Lévy space-time white noise in dimension one. For the spatial average of the solution, we prove quantitative and functional central limit theorems under m_1+m_2p<∞ for some p∈(1,3/2). These results extend the Gaussian fluctuation theory for the parabolic Anderson model to the nonlinear setting. The main new feature is a minimum-type term in the second Malliavin derivative estimate caused by the nonlinear coefficient.
ER -