Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910898645368832 |
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| author | Xia, Panqiu Zheng, Guangqu |
| author_facet | Xia, Panqiu Zheng, Guangqu |
| contents | This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for stochastic partial differential equations. We combine the second-order Gaussian Poincaré inequality with Ibragimov and Lifshits' method of characteristic functions, effectively overcoming the challenge from the lack of Itô tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07358 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises Xia, Panqiu Zheng, Guangqu Probability This short note is devoted to establishing the almost sure central limit theorem for the parabolic/hyperbolic Anderson models driven by colored-in-time Gaussian noises, completing recent results on quantitative central limit theorems for stochastic partial differential equations. We combine the second-order Gaussian Poincaré inequality with Ibragimov and Lifshits' method of characteristic functions, effectively overcoming the challenge from the lack of Itô tools in this colored-in-time setting, and achieving results that are inaccessible with previous methods. |
| title | Almost sure central limit theorems for parabolic/hyperbolic Anderson models with Gaussian colored noises |
| topic | Probability |
| url | https://arxiv.org/abs/2409.07358 |