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

作者：Toscani Giuseppe^*

来源：Physica A: Statistical Mechanics and Its Applications , 2015, 432: 35-42.

DOI：10.1016/j.physa.2015.03.018

• Entropy-power inequality
• Blachman-Stam inequality
• Costa's concavity property
• Fisher information
• Log-concave functions

We prove that the reciprocal of Fisher information of a log-concave probability density X in 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 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 (Costa, 1985).

• 出版日期2015-8-15