### 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.

Original language | English |
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Pages (from-to) | 24-34 |

Number of pages | 11 |

Journal | Journal of Applied Probability |

Volume | 34 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1997 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

### Cite this

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*Journal of Applied Probability*, vol. 34, no. 1, pp. 24-34. https://doi.org/10.1017/S002190020010066X

**Compound Poisson limit theorems for Markov chains.** / Hsiau, Shoou Ren.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Compound Poisson limit theorems for Markov chains

AU - Hsiau, Shoou Ren

PY - 1997/1/1

Y1 - 1997/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031082713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031082713&partnerID=8YFLogxK

U2 - 10.1017/S002190020010066X

DO - 10.1017/S002190020010066X

M3 - Article

VL - 34

SP - 24

EP - 34

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 1

ER -