Collapsing of non-homogeneous Markov chains

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.

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Year of publication:	2014
Authors:	Dey, Agnish ; Mukherjea, Arunava
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 84.2014, C, p. 140-148
Publisher:	Elsevier
Subject:	Non-homogeneous Markov chains \| Collapsing of Markov chains \| Reversibility \| Left invariant initial distribution

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040035