Non-reversible lifts of reversible diffusion processes and relaxation times
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911790733983744 |
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| author | Eberle, Andreas Lörler, Francis |
| author_facet | Eberle, Andreas Lörler, Francis |
| contents | We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincaré inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05041 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-reversible lifts of reversible diffusion processes and relaxation times Eberle, Andreas Lörler, Francis Probability Numerical Analysis Analysis of PDEs Statistics Theory Computation 60J25, 60J60, 60J35, 60H10, 65C40 We propose a new concept of lifts of reversible diffusion processes and show that various well-known non-reversible Markov processes arising in applications are lifts in this sense of simple reversible diffusions. Furthermore, we introduce a concept of non-asymptotic relaxation times and show that these can at most be reduced by a square root through lifting, generalising a related result in discrete time. Finally, we demonstrate how the recently developed approach to quantitative hypocoercivity based on space-time Poincaré inequalities can be rephrased and simplified in the language of lifts and how it can be applied to find optimal lifts. |
| title | Non-reversible lifts of reversible diffusion processes and relaxation times |
| topic | Probability Numerical Analysis Analysis of PDEs Statistics Theory Computation 60J25, 60J60, 60J35, 60H10, 65C40 |
| url | https://arxiv.org/abs/2402.05041 |