Compound Poisson limit theorems for Markov chains-Reference-Cited by-同舟云学术

Compound Poisson limit theorems for Markov chains

Published:1997-03 Issue:1 Volume:34 Page:24-34
ISSN:0021-9002
Container-title:Journal of Applied Probability
language:en
Short-container-title:Journal of Applied Probability

Author:

Hsiau Shoou-Ren

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.

Publisher

Cambridge University Press (CUP)

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference5 articles.

1. On the probability generating function of the sum of Markov Bernoulli random variables

2. Approximating kth-order two-state Markov chains

3. A Generalization of Poisson's Distribution for Markoff Chains

4. On the limit of the Markov binomial distribution

5. Renewal process proof for the limit of the Markov binomial distribution;Wang;Math. Sci.,1991

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Compound Poisson approximation;Probability Surveys;2022-01-01

2. Two limit theorems for Markov binomial distribution;Lithuanian Mathematical Journal;2015-07

3. Compound Poisson and signed compound Poisson approximations to the Markov binomial law;Bernoulli;2010-11-01

4. Compound Poisson limit theorems for high-level exceedances of some non-stationary processes;Bernoulli;2003-06-01

5. Random Fields on Z d , Limit Theorems and Irregular Sets;Spatial Statistics: Methodological Aspects and Applications;2001