Some harmonic functions for killed Markov branching processes with immigration and culling
| Autor: | Matija Vidmar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Primary: 60J80. Secondary: 60J50 harmonična funkcija Laplace transform Bienaymé-Galton-Watsonov proces Culling first passage downwards odbiranje Branching (linguistics) harmonic function conditioning prvi prehod navzdol branching FOS: Mathematics Applied mathematics imigracija Mathematics culling faktorizacija na minimumu Markov chain eksplozija Bienaymé–Galton–Watson process Probability (math.PR) razvejanje State (functional analysis) factorization at the minimum Laplaceova transformacija pogojevanje Harmonic function Modeling and Simulation explosion udc:519.217 Mathematics - Probability immigration |
| Zdroj: | Stochastics, vol. 94, no. 4, pp. 578-601, 2022. |
| ISSN: | 1744-2508 |
| Popis: | For a continuous-time Bienaym\'e-Galton-Watson process, $X$, with immigration and culling, $0$ as an absorbing state, call $X^q$ the process that results from killing $X$ at rate $q\in (0,\infty)$, followed by stopping it on extinction or explosion. Then an explicit identification of the relevant harmonic functions of $X^q$ allows to determine the Laplace transforms (at argument $q$) of the first passage times downwards and of the explosion time for $X$. Strictly speaking, this is accomplished only when the killing rate $q$ is sufficiently large (but always when the branching mechanism is not supercritical or if there is no culling). In particular, taking the limit $q\downarrow 0$ (whenever possible) yields the passage downwards and explosion probabilities for $X$. A number of other consequences of these results are presented. |
| Databáze: | OpenAIRE |
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