Spatial fluctuation for stochastic heat equation with H\"older coefficients

Carl Mueller; Fei Pu

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arXiv · 2510.00807

Spatial fluctuation for stochastic heat equation with H\"older coefficients

Carl Mueller·Fei Pu

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Abstract

In this paper, we establish associativity, spatial ergodicity and a central limit theorem for certain nonnegative solutions to the stochastic heat equation $\partial_t u=\frac12\partial_x^2 u+ u^\gamma \xi$ with $\gamma\in (0, 1)$. When $\gamma=\frac12$, we derive a limit for the moment generating function of the spatial integral and provide a lower bound on the spatial growth of the solution.

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Carl Mueller, Fei Pu. 2025-10-01. Spatial fluctuation for stochastic heat equation with H\"older coefficients. https://arxiv.org/abs/2510.00807

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