Linear-fractional branching processes with countably many types
Journal article, 2013
We study multi-type Bienayme-Galton-Watson processes with linear-fractional reproduction laws using various analytical tools like the contour process, spinal representation, Perron-Frobenius theorem for countable matrices, and renewal theory. For this special class of branching processes with countably many types we present a transparent criterion for R-positive recurrence with respect to the type space. This criterion appeals to the Malthusian parameter and the mean age at childbearing of the associated linear-fractional Crump-Mode-Jagers process.
Crump-Mode-Jagers process
Renewal theory
Bienayme-Galton-Watson process
R-positive recurrence
Perron-Frobenius theorem
Spinal representation
Malthusian parameter
Contour process
Multivariate linear-fractional distribution
Author
Serik Sagitov
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematical Statistics
Stochastic Processes and their Applications
0304-4149 (ISSN)
Vol. 123 8 2940-2956Stochastic models of gene and species trees
Swedish Research Council (VR) (2010-5623), 2011-01-01 -- 2013-12-31.
Subject Categories
Probability Theory and Statistics
DOI
10.1016/j.spa.2013.03.008