Conditions for the existence of a generalization of Renyi divergence

被引：5

作者：

Vigelis, Rui F. ^{[1
]}

de Andrade, Luiza H. F. ^{[2
]}

Cavalcante, Charles C. ^{[3
]}

机构：

[1] Univ Fed Ceara, Comp Engn, Campus Sobral,R Cel Estanislau Frota, BR-62010560 Sobral, CE, Brazil

[2] Fed Rural Univ Semiarid Reg, Ctr Exact & Nat Sci, Av Francisco Mota 572, BR-59625900 Mossoro, RN, Brazil

[3] Univ Fed Ceara, Teleinformat Engn Dept, Campus Pici,Bloco 722,CP 6005, BR-60440900 Fortaleza, Ceara, Brazil

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2020年 / 558卷

关键词：

Generalized divergence; Renyi entropy; Information geometry; Existence conditions; DEFORMED EXPONENTIALS; INFORMATION; SEPARATION; FAMILIES; CRITERIA;

D O I：

10.1016/j.physa.2020.124953

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We give necessary and sufficient conditions for the existence of a generalization of Renyi divergence, which is defined in terms of a deformed exponential function. If the underlying measure t is non-atomic, we found that not all deformed exponential functions can be used in the generalization of Renyi divergence; a condition involving the deformed exponential function is provided. In the case t 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. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：11

共 51 条

[1] Nonadditive generalization of the quantum Kullback-Leibler divergence for measuring the degree of purification [J].