Some limit properties for the \(m\)th-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree

DOI10.1016/j.spl.2010.03.020zbMath1196.60051OpenAlexW1993192522MaRDI QIDQ984014

Zhiyan Shi, Wei-guo Yang

Publication date: 13 July 2010

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2010.03.020

zbMATH Keywords

strong law of large numbersShannon-McMillan theorem\(m\) rooted Cayley tree\(m\)th-order nonhomogeneous Markov chain

Mathematics Subject Classification ID

Strong limit theorems (60F15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items

Strong law of large numbers for generalized sample relative entropy of non homogeneous Markov chains ⋮ The strong law of large numbers for non homogeneous M-bifurcating Markov chains indexed by a M-branch Cayley tree ⋮ Limit theorems for asymptotic circular mth-order Markov chains indexed by an m-rooted homogeneous tree ⋮ A class of small deviation theorems for the random fields on an \(m\) rooted Cayley tree ⋮ New gaps between zeros of fourth-order differential equations via Opial inequalities ⋮ The generalized entropy ergodic theorem for nonhomogeneous bifurcating Markov chains indexed by a binary tree ⋮ Asymptotic equipartition property for second-order circular Markov chains indexed by a two-rooted Cayley tree ⋮ Strong laws of large numbers for the mth-order asymptotic odd–even Markov chains indexed by an m-rooted Cayley tree ⋮ The strong law of large numbers and the Shannon-McMillan theorem for the mth-order nonhomogeneous Markov chains indexed by an m rooted Cayley tree ⋮ A class of small deviation theorems for the random variables associated withmth-order asymptotic circular Markov chains

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