Long-time behavior for discretization schemes of Fokker-Planck equations via couplings
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908641920024576 |
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| author | Jüngel, Ansgar Schuh, Katharina |
| author_facet | Jüngel, Ansgar Schuh, Katharina |
| contents | Continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations are constructed. Sufficient conditions under which quantitative exponential decay in the $ϕ$-entropy and Wasserstein distance are established, implying modified logarithmic Sobolev, Poincaré, and discrete Beckner inequalities. The results are not restricted to additive potentials and do not make use of discrete Bochner-type identities. The proof for the $ϕ$-decay relies on a coupling technique due to Conforti, while the proof for the Wasserstein distance uses the path coupling method. Furthermore, exponential equilibration for discrete-time Markov chains is proved, based on an abstract discrete Bakry-Emery method and a path coupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10111 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long-time behavior for discretization schemes of Fokker-Planck equations via couplings Jüngel, Ansgar Schuh, Katharina Probability 60J10, 60J27, 65C40, 65J08, 65M08 Continuous-time Markov chains associated to finite-volume discretization schemes of Fokker-Planck equations are constructed. Sufficient conditions under which quantitative exponential decay in the $ϕ$-entropy and Wasserstein distance are established, implying modified logarithmic Sobolev, Poincaré, and discrete Beckner inequalities. The results are not restricted to additive potentials and do not make use of discrete Bochner-type identities. The proof for the $ϕ$-decay relies on a coupling technique due to Conforti, while the proof for the Wasserstein distance uses the path coupling method. Furthermore, exponential equilibration for discrete-time Markov chains is proved, based on an abstract discrete Bakry-Emery method and a path coupling. |
| title | Long-time behavior for discretization schemes of Fokker-Planck equations via couplings |
| topic | Probability 60J10, 60J27, 65C40, 65J08, 65M08 |
| url | https://arxiv.org/abs/2403.10111 |