Chung's LIL for the linear stochastic fractional heat equation at origin
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917092257693696 |
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| author | Chang, Liu Ran, Wang |
| author_facet | Chang, Liu Ran, Wang |
| contents | Consider the linear stochastic fractional heat equation with vanishing initial condition: $$
\frac{\partial u (t,x)}{\partial t}=-(-Δ)^{\fracα2}u (t,x) + \dot{W}(t,x),\quad t> 0,\,
x\in \mathbb R, $$
where $-(-Δ)^{\fracα{2}}$ denotes the fractional Laplacian with power $α\in (1,2]$, and the driving noise $\dot W$ is a centered Gaussian field which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in\left(\frac {2-α}2,1\right)$. We establish Chung's law of the iterated logarithm for the solution at $t=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15228 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chung's LIL for the linear stochastic fractional heat equation at origin Chang, Liu Ran, Wang Probability Consider the linear stochastic fractional heat equation with vanishing initial condition: $$ \frac{\partial u (t,x)}{\partial t}=-(-Δ)^{\fracα2}u (t,x) + \dot{W}(t,x),\quad t> 0,\, x\in \mathbb R, $$ where $-(-Δ)^{\fracα{2}}$ denotes the fractional Laplacian with power $α\in (1,2]$, and the driving noise $\dot W$ is a centered Gaussian field which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in\left(\frac {2-α}2,1\right)$. We establish Chung's law of the iterated logarithm for the solution at $t=0$. |
| title | Chung's LIL for the linear stochastic fractional heat equation at origin |
| topic | Probability |
| url | https://arxiv.org/abs/2511.15228 |