The Library
Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus
Tools
Dietert, Helge, Evans, Josephine and Holding, Thomas (2018) Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus. Kinetic & Related Models, 11 (6). pp. 1427-1441. doi:10.3934/krm.2018056 ISSN 1937-5077.
|
PDF
WRAP-Convergence-equilibrium-Fokker-Planck-equation-torus-Evans-2018.pdf - Accepted Version - Requires a PDF viewer. Download (730Kb) | Preview |
Official URL: http://dx.doi.org/10.3934/krm.2018056
Abstract
We study contraction for the kinetic Fokker-Planck operator on the torus. Solving the stochastic differential equation, we show contraction and therefore exponential convergence in the Monge-Kantorovich-Wasserstein W2 distance. Finally, we investigate if such a coupling can be obtained by a co-adapted coupling, and show that then the bound must depend on the square root of the initial distance.
Item Type: | Journal Article | ||||||||
---|---|---|---|---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Heat equation -- Numerical solutions, Fokker-Planck equation, Torus (Geometry), Markov processes, Probabilities, Functional analysis | ||||||||
Journal or Publication Title: | Kinetic & Related Models | ||||||||
Publisher: | American Institute of Mathematical Sciences | ||||||||
ISSN: | 1937-5077 | ||||||||
Official Date: | December 2018 | ||||||||
Dates: |
|
||||||||
Volume: | 11 | ||||||||
Number: | 6 | ||||||||
Page Range: | pp. 1427-1441 | ||||||||
DOI: | 10.3934/krm.2018056 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Reuse Statement (publisher, data, author rights): | The following article appeared in Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus,Kinetic & Related Models,11,6,142 and may be found at http://dx.doi.org/10.3934/krm.2018056 | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 27 July 2020 | ||||||||
Date of first compliant Open Access: | 27 July 2020 | ||||||||
RIOXX Funder/Project Grant: |
|
||||||||
Open Access Version: |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year