The relative entropy and the chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these relations, their information-theoretic applications, and some generalizations pertaining to the rich class of f-divergences. Applications that are studied in this paper refer to lossless compression, the method of types and large deviations, strong data-processing inequalities, bounds on contraction coefficients and maximal correlation, and the convergence rate to stationarity of a type of discrete-time Markov chains.

中文翻译：

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关于相对熵与χ2-散度的关系、推广和应用

相对熵和卡方散度是信息论和统计学中的基本散度度量。本文的重点是研究两个散度之间的积分关系、这些关系的含义、它们的信息论应用以及与丰富的 f-散度类有关的一些概括。本文研究的应用涉及无损压缩、类型和大偏差的方法、强数据处理不等式、收缩系数和最大相关的界限，以及一类离散时间马尔可夫链的平稳收敛速度。