Markov branching processes with disasters: extinction, survival and duality to p-jump processes
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866917708298190848 |
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| author | Hermann, F. Pfaffelhuber, P. |
| author_facet | Hermann, F. Pfaffelhuber, P. |
| contents | A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for time-inhomogeneous birth-death processes underlying time-dependent binomial disasters and continuous state branching processes with $p$-jumps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_00073 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Markov branching processes with disasters: extinction, survival and duality to p-jump processes Hermann, F. Pfaffelhuber, P. Probability 60J80 (Primary) 60J75, 60F10 (Secondary) A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting results for the survival probabilities of time-homogeneous branching processes with arbitrary offspring distributions, underlying binomial disasters. Extending this method, we obtain corresponding results for time-inhomogeneous birth-death processes underlying time-dependent binomial disasters and continuous state branching processes with $p$-jumps. |
| title | Markov branching processes with disasters: extinction, survival and duality to p-jump processes |
| topic | Probability 60J80 (Primary) 60J75, 60F10 (Secondary) |
| url | https://arxiv.org/abs/1808.00073 |