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Critical Bellman-Harris branching processes with long-living particles

  • V. A. Vatutin
  • V. A. Topchii
Article

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.

Keywords

Random Walk Survival Probability STEKLOV Institute Asymptotic Representation Tauberian Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.Sobolev Institute of Mathematics (Omsk Branch)Siberian Branch of the Russian Academy of SciencesNovosibirskRussia

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