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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2606.01742 |
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| _version_ | 1866917553578704896 |
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| author | Zhang, Beibei Qian, Bin |
| author_facet | Zhang, Beibei Qian, Bin |
| contents | Consider the stochastic partial differential equation,
\begin{align*}
\partial_t u^{\varepsilon}(t\,,x) = \frac{1}{2} \partial^2_x u^{\varepsilon}(t\,,x) + b(t\,,u^{\varepsilon}(t\,,x)) + \sqrt{\varepsilon}σ(t\,,u^{\varepsilon}(t\,,x)) \dot{W}(t\,,x),
\end{align*}
where $(t\,,x)\in(0\,,\infty)\times\mathbb{R}$, and $\dot{W}$ denotes space-time white noise.
Foondun, Khoshnevisan, and Nualart \cite{FKN24} showed that this stochastic partial differential equation is well-posed under the assumptions that the initial condition $u(0)$ is bounded and measurable, while $b$ and $σ$
are locally Lipschitz continuous functions with at most linear growth. A Freidlin-Wentzell large deviation principle for the stochastic partial differential equation is established by a weak convergence approach in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01742 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large deviation principles for SPDEs with locally Lipschitz coefficients Zhang, Beibei Qian, Bin Probability Consider the stochastic partial differential equation, \begin{align*} \partial_t u^{\varepsilon}(t\,,x) = \frac{1}{2} \partial^2_x u^{\varepsilon}(t\,,x) + b(t\,,u^{\varepsilon}(t\,,x)) + \sqrt{\varepsilon}σ(t\,,u^{\varepsilon}(t\,,x)) \dot{W}(t\,,x), \end{align*} where $(t\,,x)\in(0\,,\infty)\times\mathbb{R}$, and $\dot{W}$ denotes space-time white noise. Foondun, Khoshnevisan, and Nualart \cite{FKN24} showed that this stochastic partial differential equation is well-posed under the assumptions that the initial condition $u(0)$ is bounded and measurable, while $b$ and $σ$ are locally Lipschitz continuous functions with at most linear growth. A Freidlin-Wentzell large deviation principle for the stochastic partial differential equation is established by a weak convergence approach in this paper. |
| title | Large deviation principles for SPDEs with locally Lipschitz coefficients |
| topic | Probability |
| url | https://arxiv.org/abs/2606.01742 |