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An infinite particle system with continual input and random death

Published online by Cambridge University Press:  01 July 2016

J. N. McDonald  and
N. A. Weiss
J. N. McDonald
Affiliation:
Arizona State University
N. A. Weiss
Affiliation:
Arizona State University
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Abstract

At times n = 0, 1, 2, · · · a Poisson number of particles enter each state of a countable state space. The particles then move independently according to the transition law of a Markov chain, until their death which occurs at a random time. Several limit theorems are then proved for various functionals of this infinite particle system. In particular, laws of large numbers and central limit theorems are proved.

Keywords

INFINITE PARTICLE SYSTEMSMARKOV CHAINSLAWS OF LARGE NUMBERSCENTRAL LIMIT THEOREMSRANDOM LIFETIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 4 , December 1978 , pp. 764 - 787
Copyright
Copyright © Applied Probability Trust 1978 

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