A generic approach to homogenization of a diffusion driven by growing incompressible drift
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913475015475200 |
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| author | Franke, Brice Sheu, Shuenn-Jyi |
| author_facet | Franke, Brice Sheu, Shuenn-Jyi |
| contents | We study how the resolvent-family of a diffusion behaves, as thedrift grows to infinity. The limit turns out to be a selfadjoint pseudo-resolvent.After reduction of the underlying Hilbert-space, this pseudo-resolvent becomesa resolvent to a strongly continuous semi-group of contractions. We prove thatthis semi-group is associated to some Hunt-process on some suitable state-space which is constructed from equivalence classes of the drifts trajectories.Finally, we show a distributional limit theorem for the accelerated diffusiontoward the associated Hunt process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08369 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generic approach to homogenization of a diffusion driven by growing incompressible drift Franke, Brice Sheu, Shuenn-Jyi Probability We study how the resolvent-family of a diffusion behaves, as thedrift grows to infinity. The limit turns out to be a selfadjoint pseudo-resolvent.After reduction of the underlying Hilbert-space, this pseudo-resolvent becomesa resolvent to a strongly continuous semi-group of contractions. We prove thatthis semi-group is associated to some Hunt-process on some suitable state-space which is constructed from equivalence classes of the drifts trajectories.Finally, we show a distributional limit theorem for the accelerated diffusiontoward the associated Hunt process. |
| title | A generic approach to homogenization of a diffusion driven by growing incompressible drift |
| topic | Probability |
| url | https://arxiv.org/abs/2405.08369 |