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A note on asymptotic behavior of Galton-Watson branching processes in random environments

Research paper by Han-xing Wang, Fei Zhao, Jn-yu Lu

Indexed on: 01 Apr '06Published on: 01 Apr '06Published in: Journal of Shanghai University (English Edition)



Abstract

In this paper, we investigate Galton-Watson branching processes in random environments. In the case where the environmental process is a Markov chain which is positive recurrent or has a transition matrix Q (θ,α) such that sup,, Q (θ,α) > 0 for some a, we prove that the model has the asymptotic behavior being similar to that of Galton-Watson branching processes. In other case where the environments are non-stationary independent, the sufficient conditions are obtained for certain extinction and uncertain extinction for the model.