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arXiv · 2008.04466

Conditions for the existence of a generalization of Rényi divergence

Rui F. Vigelis·Luiza H. F. de Andrade·Charles C. Cavalcante
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Abstract

We give necessary and sufficient conditions for the existence of a generalization of Rényi divergence, which is defined in terms of a deformed exponential function. If the underlying measure $μ$ is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Rényi divergence; a condition involving the deformed exponential function is provided. In the case $μ$ is purely atomic (the counting measure on the set of natural numbers), we show that any deformed exponential function can be used in the generalization.

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Rui F. Vigelis, Luiza H. F. de Andrade, Charles C. Cavalcante. 2020-08-11. Conditions for the existence of a generalization of Rényi divergence. https://doi.org/10.1016/j.physa.2020.124953

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