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Some limit theorems for positive recurrent branching Markov chains: II

Published online by Cambridge University Press:  01 July 2016

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, South Korea.

Abstract

In this paper we consider a Galton-Watson process in which particles move according to a positive recurrent Markov chain on a general state space. We prove a law of large numbers for the empirical position distribution and also discuss the rate of this convergence.

Type
General Applied Probability
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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