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Collapsing of non-homogeneous Markov chains

Author

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  • Dey, Agnish
  • Mukherjea, Arunava

Abstract

Let X(n), n≥0, be a (homogeneous) Markov chain with a finite state space S={1,2,…,m}. Let S be the union of disjoint sets S1, S2,…,Sk which form a partition of S. Define Y(n)=i if and only if X(n)∈Si for i=1,2,…,k. Is the collapsed chain Y(n) Markov? This problem was considered by Burke and Rosenblatt in 1958 and in this note this problem is studied when the X(n) chain is non-homogeneous and Markov. To the best of our knowledge, the results here are new.

Suggested Citation

  • Dey, Agnish & Mukherjea, Arunava, 2014. "Collapsing of non-homogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 140-148.
    • Handle: RePEc:eee:stapro:v:84:y:2014:i:c:p:140-148
    DOI: 10.1016/j.spl.2013.10.002
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    Cited by:

    1. Milliken, Evan, 2019. "Applications of the fundamental matrix to mean absorption and conditional mean absorption problems," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 106-115.

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