Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-26T19:52:32.827Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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