A Generalization of the Concavity of R\'{e}nyi Entropy Powe

Recently, Savar'{e}-Toscani proved that the R'{e}nyi entropy power of general probability densities solving the $p$-nonlinear heat equation in ${\mathbb{R}}^n$ is always a concave function of time, which extends Costa’s concavity inequality for Shannon’s entropy power to R'{e}nyi 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'{e}nyi 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.