Decomposition of supercritical linear-fractional branching processes
Journal article, 2013
t is well known that a supercritical single-type Bienaymé-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 Bienaymé-GaltonWatson processes with countably many types. We find explicit expressions for the main characteristics of the reproduction laws for so-called skeleton and doomed particles.
Multivariate Linear-Fractional Distribution
Dual Reproduction Law
Harris-Sevastyanov Transformation
Branching Process with Countably Many Types
Bienaymé-Galton-Watson Process
Conditioned Branching Process
Author
Serik Sagitov
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Altynay Shaimerdenova
Applied Mathematics
2152-7393 (eISSN)
Vol. 4 2 352-359Roots
Basic sciences
Areas of Advance
Life Science Engineering (2010-2018)
Subject Categories
Probability Theory and Statistics
DOI
10.4236/am.2013.42054