A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT. Issue 1 (January 2022)

• Record Type: Journal Article
• Authors: Shi, Zhiyan; Ding, Chengjun
• Is Part Of: Probability in the engineering and informational sciences. Volume 36:Issue 1(2022)
• Page Start: 169
• Page End: 183
• Publication Date: 2022-01
• Subjects: random environment -- small deviation theorems -- strong limit theorems -- tree -- uniformly bounded degree; Probabilities -- Periodicals; Engineering -- Statistical methods -- Periodicals; Information science -- Statistical methods -- Periodicals; 519.202462
• DOI: 10.1017/S026996482000042X
• Languages: English
• ISSNs: 0269-9648

Abstract

Abstract : In this paper, we mainly study a class of small deviation theorems for Markov chains indexed by an infinite tree with uniformly bounded degree in Markovian environment. Firstly, we give the definition of Markov chains indexed by a tree with uniformly bounded degree in random environment. Then, we introduce the some lemmas which are the basis of the results. Finally, a class of small deviation theorems for functionals of random fields on a tree with uniformly bounded degree in Markovian environment is established.