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.