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A CLASS OF SMALL DEVIATION THEOREMS FOR FUNCTIONALS OF RANDOM FIELDS ON A TREE WITH UNIFORMLY BOUNDED DEGREE IN RANDOM ENVIRONMENT

Published online by Cambridge University Press:  24 August 2020

Zhiyan Shi Open the ORCID record for Zhiyan Shi [Opens in a new window]  and
Chengjun Ding
Zhiyan Shi
Affiliation:
School of Mathematical Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.com
Chengjun Ding
Affiliation:
School of Mathematical Science, Jiangsu University, Zhenjiang212013, China E-mail: shizhiyan1984@126.com
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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.

Keywords

random environmentsmall deviation theoremsstrong limit theoremstreeuniformly bounded degree
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 1 , January 2022 , pp. 169 - 183
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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