Abstract.
R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the Fokker—Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional, and the Gibbs—Boltzmann entropy functional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker—Planck equation and characterize the limit as a solution to a class of variational problems.
This is a preview of subscription content, log in via an institution to check access.
Author information
Authors and Affiliations
Additional information
Accepted 2 June 2000. Online publication 6 October 2000.
Rights and permissions
About this article
Cite this article
Mikami, T. Dynamical Systems in the Variational Formulation of the Fokker—Planck Equation by the Wasserstein Metric. Appl Math Optim 42, 203–227 (2000). https://doi.org/10.1007/s002450010008
Published:
Issue Date:
DOI: https://doi.org/10.1007/s002450010008