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Exponential Decay of Rényi Divergence Under Fokker–Planck Equations

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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708, USA

    Yu Cao & Yulong Lu

  2. Department of Mathematics, Department of Physics, and Department of Chemistry, Duke University, Box 90320, Durham, NC, 27708, USA

    Jianfeng Lu

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  1. Yu Cao
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  2. Jianfeng Lu
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  3. Yulong Lu
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Correspondence to Yu Cao.

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Communicated by Eric A. Carlen.

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Cao, Y., Lu, J. & Lu, Y. Exponential Decay of Rényi Divergence Under Fokker–Planck Equations. J Stat Phys 176, 1172–1184 (2019). https://doi.org/10.1007/s10955-019-02339-8

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