Spatial fluctuation for stochastic heat equation with Hölder coefficients
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912620977586176 |
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| author | Mueller, Carl Pu, Fei |
| author_facet | Mueller, Carl Pu, Fei |
| contents | In this paper, we establish associativity, spatial ergodicity and a central limit theorem for certain nonnegative solutions to the stochastic heat equation $\partial_t u=\frac12\partial_x^2 u+ u^γξ$ with $γ\in (0, 1)$. When $γ=\frac12$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00807 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spatial fluctuation for stochastic heat equation with Hölder coefficients Mueller, Carl Pu, Fei Probability In this paper, we establish associativity, spatial ergodicity and a central limit theorem for certain nonnegative solutions to the stochastic heat equation $\partial_t u=\frac12\partial_x^2 u+ u^γξ$ with $γ\in (0, 1)$. When $γ=\frac12$, 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. |
| title | Spatial fluctuation for stochastic heat equation with Hölder coefficients |
| topic | Probability |
| url | https://arxiv.org/abs/2510.00807 |