A Dissipation of Relative Entropy by Diffusion Flows
Given a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker–Planck. Our flows of the probability measures are defined as the solution of the Fokker–Planck equation for the same strictly convex potential, which...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-12-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/19/1/9 |
| _version_ | 1828278315854594048 |
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| author | Hiroaki Yoshida |
| author_facet | Hiroaki Yoshida |
| author_sort | Hiroaki Yoshida |
| collection | DOAJ |
| description | Given a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker–Planck. Our flows of the probability measures are defined as the solution of the Fokker–Planck equation for the same strictly convex potential, which means that the flows have the same equilibrium. Then, we shall investigate the time derivative for the relative entropy in the case where the object and the reference measures are moving according to the above diffusion flows, from which we can obtain a certain dissipation formula and also an integral representation of the relative entropy. |
| first_indexed | 2024-04-13T07:29:30Z |
| format | Article |
| id | doaj.art-c0cbce7411ec4a8b9b84eaade63782a8 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T07:29:30Z |
| publishDate | 2016-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c0cbce7411ec4a8b9b84eaade63782a82022-12-22T02:56:24ZengMDPI AGEntropy1099-43002016-12-01191910.3390/e19010009e19010009A Dissipation of Relative Entropy by Diffusion FlowsHiroaki Yoshida0Department of Information Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo-ku, Tokyo 112-8610, JapanGiven a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker–Planck. Our flows of the probability measures are defined as the solution of the Fokker–Planck equation for the same strictly convex potential, which means that the flows have the same equilibrium. Then, we shall investigate the time derivative for the relative entropy in the case where the object and the reference measures are moving according to the above diffusion flows, from which we can obtain a certain dissipation formula and also an integral representation of the relative entropy.http://www.mdpi.com/1099-4300/19/1/9relative entropyrelative Fisher informationFokker–Planck equationentropy dissipationentropy gap |
| spellingShingle | Hiroaki Yoshida A Dissipation of Relative Entropy by Diffusion Flows Entropy relative entropy relative Fisher information Fokker–Planck equation entropy dissipation entropy gap |
| title | A Dissipation of Relative Entropy by Diffusion Flows |
| title_full | A Dissipation of Relative Entropy by Diffusion Flows |
| title_fullStr | A Dissipation of Relative Entropy by Diffusion Flows |
| title_full_unstemmed | A Dissipation of Relative Entropy by Diffusion Flows |
| title_short | A Dissipation of Relative Entropy by Diffusion Flows |
| title_sort | dissipation of relative entropy by diffusion flows |
| topic | relative entropy relative Fisher information Fokker–Planck equation entropy dissipation entropy gap |
| url | http://www.mdpi.com/1099-4300/19/1/9 |
| work_keys_str_mv | AT hiroakiyoshida adissipationofrelativeentropybydiffusionflows AT hiroakiyoshida dissipationofrelativeentropybydiffusionflows |