Killing versus catastrophes in birth-death processes and an application to population genetics
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918306246557696 |
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| author | Baake, Ellen Cordero, Fernando Di Gaspero, Enrico Wakolbinger, Anton |
| author_facet | Baake, Ellen Cordero, Fernando Di Gaspero, Enrico Wakolbinger, Anton |
| contents | We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes with catastrophes. The major ingredients of the proofs are a decomposition of the dynamics of these processes, a Feynman--Kac type relationship for Markov chains with reset and rebirth, and the concept of Siegmund duality, which allows us to invert the relationship between the processes. We apply our results to a pair of ancestral processes in population genetics, namely the killed ancestral selection graph and the pruned lookdown ancestral selection graph, in a finite population setting and its diffusion limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Killing versus catastrophes in birth-death processes and an application to population genetics Baake, Ellen Cordero, Fernando Di Gaspero, Enrico Wakolbinger, Anton Probability 60J80, 60J90, 60J25, 92D15 We establish connections between the absorption probabilities of a class of birth-death processes with killing, and the stationary tail of a related class of birth-death processes with catastrophes. The major ingredients of the proofs are a decomposition of the dynamics of these processes, a Feynman--Kac type relationship for Markov chains with reset and rebirth, and the concept of Siegmund duality, which allows us to invert the relationship between the processes. We apply our results to a pair of ancestral processes in population genetics, namely the killed ancestral selection graph and the pruned lookdown ancestral selection graph, in a finite population setting and its diffusion limit. |
| title | Killing versus catastrophes in birth-death processes and an application to population genetics |
| topic | Probability 60J80, 60J90, 60J25, 92D15 |
| url | https://arxiv.org/abs/2407.08478 |