Laws of Large Numbers for the Occupation Time of an Age-Dependent Critical Binary Branching System

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dc.creatorLópez-Mimbela, José Alfredo
dc.creatorSalas, Antonio Murillo
dc.date2009-03-10
dc.date.accessioned2026-07-07T12:51:34Z
dc.date.available2026-07-07T12:51:34Z
dc.descriptionThe occupation time of an age-dependent branching particle system in $\Rd$ is considered, where the initial population is a Poisson random field and the particles are subject to symmetric $α$-stable migration, critical binary branching and random lifetimes. Two regimes of lifetime distributions are considered: lifetimes with finite mean and lifetimes belonging to the normal domain of attraction of a $γ$-stable law, $γ\in(0,1)$. It is shown that in dimensions $d>αγ$ for the heavy-tailed lifetimes case, and $d>α$ for finite mean lifetimes, the occupation time proccess satisfies a strong law of large numbers.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0903.1871
dc.identifierhttp://arxiv.org/abs/0903.1871
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223027
dc.subjectProbability
dc.subject60J80; 60F15
dc.titleLaws of Large Numbers for the Occupation Time of an Age-Dependent Critical Binary Branching System
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