Article ID Journal Published Year Pages File Type
974273 Physica A: Statistical Mechanics and its Applications 2015 8 Pages PDF
Abstract

•We consider the entropy power of the sum X+ZtX+Zt, where ZtZt is a Gaussian noise.•If XX has a log-concave density. We extend Costa’s result on concavity.•For log-concave densities the third derivative of entropy power has a positive sign.•Also, the reciprocal of Fisher information of X+ZtX+Zt is concave.

We prove that the reciprocal of Fisher information of a log-concave probability density XX in RnRn is concave in tt with respect to the addition of a Gaussian noise Zt=N(0,tIn)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 XX in RnRn is nonnegative in tt with respect to the addition of a Gaussian noise ZtZt. For log-concave densities this improves the well-known Costa’s concavity property of the entropy power (Costa, 1985).

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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