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arXiv · 1410.2722

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

G. Toscani
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Abstract

We prove that the reciprocal of Fisher information of a log-concave probability density $X$ in ${\bf{R}}^n$ is concave in $t$ with respect to the addition of a Gaussian noise $Z_t = N(0, tI_n)$. As a byproduct of this result we show that the third derivative of the entropy power of a log-concave probability density $X$ in ${\bf{R}}^n$ is nonnegative in $t$ with respect to the addition of a Gaussian noise $Z_t$. For log-concave densities this improves the well-known Costa's concavity property of the entropy power.

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G. Toscani. 2014-10-10. A concavity property for the reciprocal of Fisher information and its consequences on Costa's EPI. https://doi.org/10.1016/j.physa.2015.03.018

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