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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, Zhenjiang 212013, China E-mail: shizhiyan1984@126.com
Chengjun Ding
Affiliation:
School of Mathematical Science, Jiangsu University, Zhenjiang 212013, 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

Information

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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