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Compound Poisson limit theorems for Markov chains

  • Shoou-Ren Hsiau (a1)

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.

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Postal address: Department of Mathematics, National Changhua University of Education, Changhua, Taiwan 50058, Republic of China.

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

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References

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Gani, J. (1982) On the probability generating function of the sum of Markov Bernoulli random variables. J. Appl. Prob. 19A, 321326.
Koopman, B. O. (1950) A generalization of Poisson's distribution for Markov chains. Proc. Nat. Acad. Sci. 36, 202207.
Wang, Y. H. (1981) On the limit of the Markov binomial distribution. J. Appl. Prob. 18, 937942.
Wang, Y. H. (1992) Approximating kth-order two-state Markov chains. J. Appl. Prob. 29, 861868.
Wang, Y. H. and Bühler, W. J. (1991) Renewal process proof for the limit of the Markov binomial distribution. Math. Sci. 16, 6668.

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Compound Poisson limit theorems for Markov chains

  • Shoou-Ren Hsiau (a1)

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