Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917261199015936 |
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| author | Arnold, Anton Einav, Amit Wöhrer, Tobias |
| author_facet | Arnold, Anton Einav, Amit Wöhrer, Tobias |
| contents | The goal of this work is to find the sharp rate of convergence to equilibrium under the quadratic Fisher information functional for solutions to Fokker-Planck equations governed by a constant drift term and a constant, yet possibly degenerate, diffusion matrix. A key ingredient in our investigation is a recent work of Arnold, Signorello, and Schmeiser, where the $L^2$-propagator norm of such Fokker-Planck equations was shown to be identical to the propagator norm of a finite dimensional ODE which is determined by matrices that are intimately connected to those appearing in the associated Fokker-Planck equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05316 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations Arnold, Anton Einav, Amit Wöhrer, Tobias Analysis of PDEs 35Q84, 35H10, 35K10, 35B40 The goal of this work is to find the sharp rate of convergence to equilibrium under the quadratic Fisher information functional for solutions to Fokker-Planck equations governed by a constant drift term and a constant, yet possibly degenerate, diffusion matrix. A key ingredient in our investigation is a recent work of Arnold, Signorello, and Schmeiser, where the $L^2$-propagator norm of such Fokker-Planck equations was shown to be identical to the propagator norm of a finite dimensional ODE which is determined by matrices that are intimately connected to those appearing in the associated Fokker-Planck equations. |
| title | Sharp Decay of the Fisher Information for Degenerate Fokker-Planck Equations |
| topic | Analysis of PDEs 35Q84, 35H10, 35K10, 35B40 |
| url | https://arxiv.org/abs/2309.05316 |