International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 694285, 24 pages
http://dx.doi.org/10.1155/2012/694285
Research Article

A Decomposable Branching Process in a Markovian Environment

Vladimir Vatutin,1 Elena Dyakonova,1 Peter Jagers,2 and Serik Sagitov2

1Steklov Mathematical Institute, Russian Academy of Sciences, Moscow 119991, Russia
2Chalmers University of Technology and University of Gothenberg, 412 96 Gothenburg, Sweden

Received 28 September 2012; Accepted 18 December 2012

Academic Editor: Peter Olofsson

Copyright © 2012 Vladimir Vatutin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A population has two types of individuals, with each occupying an island. One of those, where individuals of type 1 live, offers a variable environment. Type 2 individuals dwell on the other island, in a constant environment. Only one-way migration ( ) is possible. We study then asymptotics of the survival probability in critical and subcritical cases.