Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914123952947200 |
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| author | Li, Xinpeng Yu, Miao |
| author_facet | Li, Xinpeng Yu, Miao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26066 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures Li, Xinpeng Yu, Miao Probability 60B10, 60E05, 60E15 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. |
| title | Generalized Divergence Measures and Weak Convergence for the Sets of Probability Measures |
| topic | Probability 60B10, 60E05, 60E15 |
| url | https://arxiv.org/abs/2510.26066 |