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has been cited by the following article:
TITLE: Decomposition of Supercritical Linear-Fractional Branching Processes
AUTHORS: Serik Sagitov, Altynay Shaimerdenova
KEYWORDS: Harris-Sevastyanov Transformation; Dual Reproduction Law; Branching Process with Countably Many Types; Multivariate Linear-Fractional Distribution; Bienaymé-Galton-Watson Process; Conditioned Branching Process
JOURNAL NAME: Applied Mathematics, Vol.4 No.2, February 27, 2013
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.