Work

Central limit theorems for stochastic heat equation driven by Gaussian noise with heat-kernel covariance

Year: 2026

Type: preprint

Abstract: In this article, we study the spatial fluctuations of the Skorohod solution to a stochastic heat equation on $\mathbb R^d$ for $d<4$, driven by multiplicative Gaussian noise with the non-separable covariance kernel $p_{|t-s|}(x-y)$. We prove that the solution is strictly stationary and spatially ergodic at every fixed time. For the centered spatial integral $F_R(t)=\int_{\{|x|

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.04941

Authors: Wang, Meng, Yuan, Wangjun

Institution: Southern University of Science and Technology

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Guangdong Science and Technology Department, Basic and Applied Basic Research Foundation of Guangdong Province

OpenAlex ID: W7220649795

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