Collapsing of non-homogeneous Markov chains

Agnish Dey and Arunava Mukherjea

Statistics & Probability Letters, 2014, vol. 84, issue C, 140-148

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.

Keywords: Non-homogeneous Markov chains; Collapsing of Markov chains; Reversibility; Left invariant initial distribution (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2013.10.002

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