The strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Issue 15 (8th July 2021)

• Record Type: Journal Article
• Authors: Ding, Chengjun; Shi, Zhiyan; Yang, Weiguo
• Is Part Of: Communications in statistics. Volume 50:Issue 15(2021)
• Page Start: 3573
• Page End: 3585
• Publication Date: 2021-07-08
• Subjects: Tree -- uniformly bounded degree -- random environment -- strong law of large numbers -- Shannon-McMillan theorem; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1708398
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we are going to study the strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Firstly, we give the definition of Markov chains indexed by an infinite tree with uniformly bounded degree in random environment. Then, we establish some strong limit theorems that are the basis of the main result. Finally, we prove the strong law of large numbers and Shannon-McMillan theorem for Markov chains indexed by an infinite tree with uniformly bounded degree in Markovian environment.