A Generalization of the Concavity of R\'enyi Entropy Powe
Abstract
Recently, Savar\'e-Toscani proved that the R\'enyi entropy power of general probability densities solving the p-nonlinear heat equation in Rn is always a concave function of time, which extends Costa's concavity inequality for Shannon's entropy power to R\'enyi entropies. In this paper, we give a generalization of Savar\'e-Toscani's result by giving a class of sufficient conditions of the parameters under which the concavity of the R\'enyi entropy power is still valid. These conditions are quite general and include the parameter range given by Savar\'e-Toscani as special cases. Also, the conditions are obtained with a systematical approach.
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