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Compound Poisson limit theorems for Markov chains

Part of: Limit theorems Distribution theory - Probability Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  14 July 2016

Shoou-Ren Hsiau
Shoou-Ren Hsiau*
Affiliation:
National Changhua University of Education
*
∗ Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, Republic of China.
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Abstract

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.

Keywords

POISSON LIMIT THEOREMCOMPOUND POISSON LIMIT THEOREMPROBABILITY GENERATING FUNCTIONCHARACTERISTIC FUNCTIONMARKOV CHAIN

MSC classification

Primary: 60B10: Convergence of probability measures 60F17: Functional limit theorems; invariance principles
Secondary: 60E10: Characteristic functions; other transforms 60E05: Distributions

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 24 - 34
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This research is supported by National Science Council of Republic of China.

References

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