Transportation cost inequalities for stochastic reaction diffusion equations on the whole line $\mathbb{R}$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866912227094691840 |
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| author | Li, Yue Shang, Shijie Zhang, Tusheng |
| author_facet | Li, Yue Shang, Shijie Zhang, Tusheng |
| contents | In this paper, we established quadratic transportation cost inequalities for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise on the whole line $\mathbb{R}$. Since the space variable is defined on the unbounded domain $\mathbb{R}$, the inequalities are proved under a weighted $L^2$-norm and a weighted uniform metric in the so called $L^2_{tem}$, $C_{tem}$ spaces. The new moments estimates of the stochastic convolution with respect to space-time white noise play an important role. In addition, the transportation cost inequalities are also obtained for the stochastic reaction diffusion equations with random initial values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19739 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transportation cost inequalities for stochastic reaction diffusion equations on the whole line $\mathbb{R}$ Li, Yue Shang, Shijie Zhang, Tusheng Probability 60H15 (Primary) 35R60 (Secondary) In this paper, we established quadratic transportation cost inequalities for solutions of stochastic reaction diffusion equations driven by multiplicative space-time white noise on the whole line $\mathbb{R}$. Since the space variable is defined on the unbounded domain $\mathbb{R}$, the inequalities are proved under a weighted $L^2$-norm and a weighted uniform metric in the so called $L^2_{tem}$, $C_{tem}$ spaces. The new moments estimates of the stochastic convolution with respect to space-time white noise play an important role. In addition, the transportation cost inequalities are also obtained for the stochastic reaction diffusion equations with random initial values. |
| title | Transportation cost inequalities for stochastic reaction diffusion equations on the whole line $\mathbb{R}$ |
| topic | Probability 60H15 (Primary) 35R60 (Secondary) |
| url | https://arxiv.org/abs/2305.19739 |