Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree

DOI10.1186/1029-242X-2012-2zbMath1273.60035WikidataQ59290659 ScholiaQ59290659MaRDI QIDQ366179

Zhiyan Shi, Lixin Tian, Qing Pei Zang, Wei-guo Yang

Publication date: 12 September 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

zbMATH Keywords

strong law of large numbersShannon-McMillan theoremsecond-order Markov chainuniformly bounded tree

Mathematics Subject Classification ID

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

Related Items

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

Cites Work

• Strong law of large numbers for Markov chains indexed by an infinite tree with uniformly bounded degree
• Automorphism invariant measures on trees
• Markov chains indexed by trees
• Some limit properties for Markov chains indexed by a homogeneous tree.
• Strong law of large numbers for Markov chains field on a Bethe tree
• The Asymptotic Equipartition Property for<tex>$M$</tex>th-Order Nonhomogeneous Markov Information Sources
• Entropic aspects of random fields on trees