Variational formulation of the Fokker-Planck equation with decay: a particle approach
Analysis of PDEs
2013-03-08 v3 Functional Analysis
Probability
Abstract
We introduce a stochastic particle system that corresponds to the Fokker-Planck equation with decay in the many-particles limit, and study its large deviations. We show that the large-deviation rate functional corresponds to an energy-dissipation functional in a Gamma-convergence sense. Moreover, we prove that the resulting functional, which involves entropic terms and the Wasserstein metric, is again a variational formulation for the Fokker-Planck equation with decay.
Keywords
Cite
@article{arxiv.1108.3181,
title = {Variational formulation of the Fokker-Planck equation with decay: a particle approach},
author = {Mark Peletier and Michiel Renger and Marco Veneroni},
journal= {arXiv preprint arXiv:1108.3181},
year = {2013}
}