Exponential decay of R\'enyi divergence under Fokker-Planck equations
Analysis of PDEs
2019-06-19 v2
Abstract
We prove the exponential convergence to the equilibrium, quantified by R\'enyi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential decay result on the relative entropy for the same equation.
Keywords
Cite
@article{arxiv.1805.06554,
title = {Exponential decay of R\'enyi divergence under Fokker-Planck equations},
author = {Yu Cao and Jianfeng Lu and Yulong Lu},
journal= {arXiv preprint arXiv:1805.06554},
year = {2019}
}
Comments
Exponential convergence rate in Theorem 1.2 has been improved and a simpler proof is provided