Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures

Xinpeng Li; Miao Yu

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arXiv · 2510.26066

Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures

Xinpeng Li·Miao Yu

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Abstract

This paper extends the asymmetric Kullback-Leibler divergence and symmetric Jensen-Shannon divergence from two probability measures to the case of two sets of probability measures. We establish some fundamental properties of these generalized divergences, including a duality formula and a Pinsker-type inequality. Furthermore, convergence results are derived for both the generalized asymmetric and symmetric divergences, as well as for weak convergence under sublinear expectations.

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Xinpeng Li, Miao Yu. 2025-10-30. Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures. https://arxiv.org/abs/2510.26066

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