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Poisson theorem for non-homogeneous Markov chains

Published online by Cambridge University Press:  14 July 2016

Janusz Pawłowski
Janusz Pawłowski*
Affiliation:
University of Wroclaw
*
∗Postal address: Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50–384 Wrocław, Poland.
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Abstract

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

Keywords

COMPOUND POISSON DISTRIBUTIONTRANSITION PROBABILITIES
Type
Short Communications
Information
Journal of Applied Probability , Volume 26 , Issue 3 , September 1989 , pp. 637 - 642
Copyright
Copyright © Applied Probability Trust 1989 

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References

Baisakalov, I. B. (1968) Poisson's law for a nonstationary Markov chain. (Russian: Kazakh summary) Izv. Akad. Nauk Kazah. SSR, Ser. Fiz-Mat. 5, 42–47.Google Scholar
Gani, J. (1982) On the probability generating function of the sum of Markov Bernoulli random variables. J. Appl. Prob. 19A, 321–326.CrossRefGoogle Scholar
Macis, Ju. Ju. (1979) Bernoulli trials with variable probabilities. (Russian: Lithuanian and English summaries) Litovsk. Mat. Sb. 19, 145–151.Google Scholar
Wang, Y. H. (1981) On the limit of the Markov binomial distribution. J. Appl. Prob. 18, 937–942.CrossRefGoogle Scholar