A sufficient condition for a unique invariant distribution of a higher-order Markov chain

Bernhard C. Geiger

Statistics & Probability Letters, 2017, vol. 130, issue C, 49-56

Abstract: We derive a sufficient condition for a kth order homogeneous Markov chain Z with finite alphabet Z to have a unique invariant distribution on Zk. Specifically, let X be a first-order, stationary Markov chain with finite alphabet X and a single recurrent class, let g:X→Z be non-injective, and define the (possibly non-Markovian) process Y:=g(X) (where g is applied coordinate-wise). If Z is the kth order Markov approximation of Y, its invariant distribution is unique. We generalize this to non-Markovian processes X.

Keywords: Markov chains; Invariant distribution; Function of Markov chains (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1016/j.spl.2017.07.006

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