Some limit properties for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree

Zhiyan Shi and Weiguo Yang

Statistics & Probability Letters, 2010, vol. 80, issue 15-16, 1223-1233

Abstract: In this paper, we first study a convergence theorem for a finite mth-order nonhomogeneous Markov chain indexed by an m rooted Cayley tree. As corollaries, we obtain some limit theorems for the frequencies of occurrence of states for this Markov chain. Finally, we obtain the strong law of large numbers (LLN) and the Shannon-McMillan theorem for a class of finite mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree.

Keywords: m; rooted; Cayley; tree; mth-order; nonhomogeneous; Markov; chain; Strong; law; of; large; numbers; Shannon-McMillan; theorem (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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