Critical Bellman-Harris branching processes with long-living particles View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2013-10

AUTHORS

V. A. Vatutin, V. A. Topchii

ABSTRACT

A critical indecomposable two-type Bellman-Harris branching process is considered in which the life-length of the first-type particles has finite variance while the tail of the life-length distribution of the second-type particles is regularly varying at infinity with parameter β ∈ (0, 1]. It is shown that, contrary to the critical indecomposable Bellman-Harris branching processes with finite variances of the life-lengths of particles of both types, the probability of observing first-type particles at a distant moment t is infinitesimally less than the survival probability of the whole process. In addition, a Yaglom-type limit theorem is proved for the distribution of the number of the first-type particles at moment t given that the population contains particles of the first type at this moment. More... »

PAGES

243-272

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s0081543813060199

DOI

http://dx.doi.org/10.1134/s0081543813060199

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040034858


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