Utilize este identificador para referenciar este registo: http://hdl.handle.net/1822/32283

TítuloSkeletons of near-critical Bienaymé-Galton-Watson branching processes
AutorSagitov, Serik
Serra, Maria Conceição
Palavras-chaveBienaymé-Galton-Watson process
Decomposable multi-type branching process
Birth and death process
Escape from extinction
Data2015
EditoraApplied Probability Trust
CitaçãoSagitov, S., & Serra, M. C. (2015). Skeletons of near-critical Bienaymé-Galton-Watson branching processes. Advances in Applied Probability, 47(2), 530-544
ResumoSkeletons of branching processes are defined as trees of lineages characterized by an appropriate signature of future reproduction success. In the supercritical case a natural choice is to look for the lineages that survive forever [6]. In the critical case it was earlier suggested [7] to distinguish the particles with the total number of descendants exceeding a certain threshold. These two definitions lead to asymptotic representations of the skeletons as either pure birth process (in the slightly supercritical case) or critical birth-death processes (in the critical case conditioned on the total number of particles exceeding a high threshold value). The limit skeletons reveal typical survival scenarios for the underlying branching processes. In this paper we consider near-critical Bienaym´e-Galton-Watson processes and define their skeletons using marking of particles. If marking is rare, such skeletons are approximated by birth and death processes which can be subcritical, critical or supercritical. We obtain the limit skeleton for a sequential mutation model [8] and compute the density distribution function for the time to escape from extinction.
Tipoarticle
URIhttp://hdl.handle.net/1822/32283
ISSN0001-8678
Arbitragem científicayes
AcessorestrictedAccess
Aparece nas coleções:CMAT - Artigos com arbitragem/Papers with refereeing

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