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A concavity property for the reciprocal of Fisher information and its consequences on Costa’s EPI

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  • Toscani, Giuseppe

Abstract

We prove that the reciprocal of Fisher information of a log-concave probability density X in Rn is concave in t with respect to the addition of a Gaussian noise Zt=N(0,tIn). As a byproduct of this result we show that the third derivative of the entropy power of a log-concave probability density X in Rn is nonnegative in t with respect to the addition of a Gaussian noise Zt. For log-concave densities this improves the well-known Costa’s concavity property of the entropy power (Costa, 1985).

Suggested Citation

  • Toscani, Giuseppe, 2015. "A concavity property for the reciprocal of Fisher information and its consequences on Costa’s EPI," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 35-42.
    • Handle: RePEc:eee:phsmap:v:432:y:2015:i:c:p:35-42
    DOI: 10.1016/j.physa.2015.03.018
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