Scaling limit of a long-range random walk in time-correlated random environment
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917791108431872 |
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| author | Rang, Guanglin Song, Jian Wang, Meng |
| author_facet | Rang, Guanglin Song, Jian Wang, Meng |
| contents | This paper concerns a long-range random walk in random environment in dimension $1+1$, where the environmental disorder is independent in space but has long-range correlations in time. We prove that two types of rescaled partition functions converge weakly to the Stratonovich solution and the Itô-Skorohod solution respectively of a fractional stochastic heat equation with multiplicative Gaussian noise which is white in space and colored in time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01009 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scaling limit of a long-range random walk in time-correlated random environment Rang, Guanglin Song, Jian Wang, Meng Probability This paper concerns a long-range random walk in random environment in dimension $1+1$, where the environmental disorder is independent in space but has long-range correlations in time. We prove that two types of rescaled partition functions converge weakly to the Stratonovich solution and the Itô-Skorohod solution respectively of a fractional stochastic heat equation with multiplicative Gaussian noise which is white in space and colored in time. |
| title | Scaling limit of a long-range random walk in time-correlated random environment |
| topic | Probability |
| url | https://arxiv.org/abs/2210.01009 |