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Some harmonic functions for killed Markov branching processes with immigration and cullingVidmar, Matija, 1988-Za Bienaymé-Galton-Watsonov proces v zveznem času, ▫$X$▫, z imigracijo in odbiranjem, ▫$0$▫ kot absorbirajočem stanju, recimo ▫$X^q$▫ procesu, ki ga dobimo tako, da ubijamo ▫$X$▫ z intenziteto ▫$q$▫, ... nato pa ga še ustavimo, ko izumre ali eksplodira. Eksplicitna identifikacija relevantnih harmoničnih funkcij za ▫$X^q$▫ nam potem omogoči določitev Laplaceovih transformirank (pri argumentu ▫$q$▫) časov prvih prehodov navzdol kot tudi časa eksplozije ▫$X$▫. Če smo čisto natančni, je to storjeno samo, ko je intenziteta ubijanja ▫$q$▫ dovolj velika (vendar vedno kadar mehanizem razvejanja ni superkritičen ali ko ni odbiranja). V posebnem, če vzamemo limito, ko gre ▫$q$▫ proti ▫$0$▫ (kadar je to možno) dobimo verjetnosti izumrtja in eksplozij za ▫$X$▫. Predstavimo še nekaj drugih posledic teh rezultatov.Source: Stochastics. - ISSN 1744-2508 (Vol. 94, iss. 4, 2022, str. 578-601)Type of material - article, component part ; adult, seriousPublish date - 2022Language - englishCOBISS.SI-ID - 73746947
Author
Vidmar, Matija, 1988-
Topics
Bienaymé-Galton-Watsonov proces |
razvejanje |
imigracija |
odbiranje |
harmonična funkcija |
prvi prehod navzdol |
eksplozija |
Laplaceova transformacija |
faktorizacija na minimumu |
pogojevanje |
Bienaymé-Galton-Watson process |
branching |
immigration |
culling |
harmonic function |
first passage downwards |
explosion |
Laplace transform |
factorization at the minimum |
conditioning
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