Population Size Dependent Generalized Multitype Branching Processes

Abstract

In this paper, we introduce the population size dependent generalized multitype branching process. This is a Markovian model that allows us to study homogeneous multitype branching processes in a unified way. The basic properties for this model, transitions between its states, as well as the existence of a stationary limiting distribution, are investigated. Finally, we apply the obtained results to a new controlled multitype branching process.

Keywords:

• Homogeneous multitype Markov chains
• Multitype branching processes

Mathematics Subject Classification:

• Primary 60J10
• Secondary 60J80

ACKNOWLEDGMENTS

The authors would like to thank the anonymous referee for his/her interesting and helpful comments.

This research has been supported by the Ministerio de Ciencia y Tecnología and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2003-06074.