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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.10068 |
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| _version_ | 1866916521739026432 |
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| author | Cardoso, Pedro Gonçalves, Patrícia |
| author_facet | Cardoso, Pedro Gonçalves, Patrícia |
| contents | The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional fractional Laplacian. The approach is to consider a boundary driven exclusion process with long jumps and asymmetric jump rates. Depending on the strength of the asymmetry we prove the convergence to stationary solutions of either the Ornstein-Uhlenbeck equation, or the stochastic Burgers equation. In the later setting, the convergence in some regimes is guaranteed by the recent proof of uniqueness of energy solutions derived in [16]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regional Fractional Stochastic Burgers from random interactions Cardoso, Pedro Gonçalves, Patrícia Probability The purpose of this article is to derive the crossover from the Ornstein-Uhlenbeck process to energy solutions of the stochastic Burgers equation with characteristic operators given in terms of fractional operators, such as the regional fractional Laplacian. The approach is to consider a boundary driven exclusion process with long jumps and asymmetric jump rates. Depending on the strength of the asymmetry we prove the convergence to stationary solutions of either the Ornstein-Uhlenbeck equation, or the stochastic Burgers equation. In the later setting, the convergence in some regimes is guaranteed by the recent proof of uniqueness of energy solutions derived in [16]. |
| title | Regional Fractional Stochastic Burgers from random interactions |
| topic | Probability |
| url | https://arxiv.org/abs/2412.10068 |