Reversible Markov kernels and involutions on product spaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913469629988864 |
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| author | Piccioni, Mauro Wesołowski, Jacek |
| author_facet | Piccioni, Mauro Wesołowski, Jacek |
| contents | In this paper the relations between independence preserving (IP) involutions and reversible Markov kernels are investigated. We introduce an involutive augmentation H = (f, g_f) of a measurable function f and relate the IP property of H to f-generated reversible Markov kernels. Various examples appeared in the literature are presented as particular cases of the construction. In particular, we prove that the IP property generated by the (reversible) Markov kernel of random walk with a reflecting barrier at the origin characterizes geometric-type laws |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reversible Markov kernels and involutions on product spaces Piccioni, Mauro Wesołowski, Jacek Probability 60J05, 60G10, 60E05, 62E10 In this paper the relations between independence preserving (IP) involutions and reversible Markov kernels are investigated. We introduce an involutive augmentation H = (f, g_f) of a measurable function f and relate the IP property of H to f-generated reversible Markov kernels. Various examples appeared in the literature are presented as particular cases of the construction. In particular, we prove that the IP property generated by the (reversible) Markov kernel of random walk with a reflecting barrier at the origin characterizes geometric-type laws |
| title | Reversible Markov kernels and involutions on product spaces |
| topic | Probability 60J05, 60G10, 60E05, 62E10 |
| url | https://arxiv.org/abs/2408.08646 |