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Journal of Statistical Physics

, Volume 176, Issue 5, pp 1172–1184 | Cite as

Exponential Decay of Rényi Divergence Under Fokker–Planck Equations

  • Yu CaoEmail author
  • Jianfeng Lu
  • Yulong Lu
Article

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.

Keywords

Rényi divergence Fokker–Planck equation Exponential convergence Gradient flow 

Notes

Acknowledgements

The work of YC and JL is supported in part by the National Science Foundation under grant DMS-1454939.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of Mathematics, Department of Physics, and Department of ChemistryDuke UniversityDurhamUSA

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