Some harmonic functions for killed Markov branching processes with immigration and culling

Vidmar, Matija (avtor)

For a continuous-time Bienaymé-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.

• Jezik: Angleški jezik
• Ključne besede: Bienaymé–Galton–Watson process, branching, immigration, culling, harmonic function, first passage downwards, explosion, Laplace transform, factorization at the minimum, conditioning
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2022
• Št. strani: Str. 578-601
• Številčenje: Vol. 94, no. 4
• PID: 20.500.12556/RUL-141243
• UDK: 519.217
• ISSN pri članku: 1744-2508
• DOI: 10.1080/17442508.2021.1963249
• COBISS.SI-ID: 73746947
• Datum objave v RUL: 26.09.2022

VIDMAR, Matija, 2022, Some harmonic functions for killed Markov branching processes with immigration and culling. Stochastics [na spletu]. 2022. Vol. 94, no. 4, p. 578–601. [Dostopano 7 april 2025]. DOI 10.1080/17442508.2021.1963249. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=141243

Gradivo je del revije

• Naslov: Stochastics
• Založnik: Taylor & Francis
• ISSN: 1744-2508
• COBISS.SI-ID: 513295129

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: Bienaymé-Galton-Watsonov proces, razvejanje, imigracija, odbiranje, harmonična funkcija, prvi prehod navzdol, eksplozija, Laplaceova transformacija, faktorizacija na minimumu, pogojevanje

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika