Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on $\mathbb{R}$ driven by space-time white noise
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917918049042432 |
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| author | Li, Yue Shang, Shijie Zhai, Jianliang |
| author_facet | Li, Yue Shang, Shijie Zhai, Jianliang |
| contents | In this paper, we consider stochastic reaction-diffusion equations with super-linear drift on the real line $\mathbb{R}$ driven by space-time white noise. A Freidlin-Wentzell large deviation principle is established by a modified weak convergence method on the space $C([0,T], C_{tem}(\mathbb{R}))$. Obtaining the main result in this paper is challenging due to the setting of unbounded domain, the space-time white noise, and the superlinear drift term without dissipation. To overcome these difficulties, the special designed norm on $C([0,T], C_{tem}(\mathbb{R}))$, one order moment estimates of the stochastic convolution and two nonlinear Gronwall-type inequalities play an important role. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_14554 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on $\mathbb{R}$ driven by space-time white noise Li, Yue Shang, Shijie Zhai, Jianliang Probability 60H15, 60F10 In this paper, we consider stochastic reaction-diffusion equations with super-linear drift on the real line $\mathbb{R}$ driven by space-time white noise. A Freidlin-Wentzell large deviation principle is established by a modified weak convergence method on the space $C([0,T], C_{tem}(\mathbb{R}))$. Obtaining the main result in this paper is challenging due to the setting of unbounded domain, the space-time white noise, and the superlinear drift term without dissipation. To overcome these difficulties, the special designed norm on $C([0,T], C_{tem}(\mathbb{R}))$, one order moment estimates of the stochastic convolution and two nonlinear Gronwall-type inequalities play an important role. |
| title | Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on $\mathbb{R}$ driven by space-time white noise |
| topic | Probability 60H15, 60F10 |
| url | https://arxiv.org/abs/2307.14554 |