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| Autor Principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2202.04534 |
| Tags: |
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Table of Contents:
- We consider the stochastic heat equation on the 1-dimensional torus $\mathbb{T}:=\left[-1,1\right]$ with periodic boundary conditions: $$ \partial_t u(t,x)=\partial^2_x u(t,x)+σ(t,x,u)\dot{F}(t,x),\quad x\in \mathbb{T},t\in\mathbb{R}_+, $$ where $\dot{F}(t,x)$ is a generalized Gaussian noise, which is white in time and colored in space. Assuming that $σ$ is Lipschitz in $u$ and uniformly bounded, we estimate small ball probabilities for the solution $u$ when $u(0,x)\equiv 0$.