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Some limit theorems for positive recurrent branching Markov chains: I

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  01 July 2016

Krishna B. Athreya  and
Hye-Jeong Kang
Krishna B. Athreya*
Affiliation:
Iowa State University
Hye-Jeong Kang*
Affiliation:
Seoul National University
*
∗ Postal address: Departments of Mathematics and Statistics, Iowa State University, Ames, Iowa 50011, USA. Email address: [email protected]
∗∗ Postal address: Global Analysis Research Center, Department of Mathematics, Seoul National University, Seoul 151-742, Korea.
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Abstract

In this paper we consider a Galton-Watson process whose particles move according to a Markov chain with discrete state space. The Markov chain is assumed to be positive recurrent. We prove a law of large numbers for the empirical position distribution and also discuss the large deviation aspects of this convergence.

Keywords

Positive recurrent Markov chainsGalton-Watson processeslaw of large numberslarge deviation

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F10: Large deviations
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 3 , September 1998 , pp. 693 - 710
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Research supported in part by a National Science Foundation Grant #DMS 9204938.

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