Exponential Decay of Rényi Divergence Under Fokker–Planck Equations

Yu Cao, Jianfeng Lu, Yulong Lu

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

We prove the exponential convergence to the equilibrium, quantified by Rényi 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.

Original languageEnglish (US)
Pages (from-to)1172-1184
Number of pages13
JournalJournal of Statistical Physics
Volume176
Issue number5
DOIs
StatePublished - Sep 1 2019
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Exponential convergence
  • Fokker–Planck equation
  • Gradient flow
  • Rényi divergence

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