Decomposition of Supercritical Linear-Fractional Branching Processes

Serik Sagitov, Altynay Shaimerdenova

Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Almaty, Kazakhstan.
Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden.

DOI: 10.4236/am.2013.42054                

Abstract

It is well known that a supercritical single-type Bienayme-Galton-Watson process can be viewed as a decomposable branching process formed by two subtypes of particles: those having infinite line of descent and those who have finite number of descendants. In this paper we analyze such a decomposition for the linear-fractional Bienayme-Galton-Watson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.

Keywords

Harris-Sevastyanov Transformation; Dual Reproduction Law; Branching Process with Countably Many Types; Multivariate Linear-Fractional Distribution; Bienaymé-Galton-Watson Process; Conditioned Branching Process

Conflicts of Interest

The authors declare no conflicts of interest.

References

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