A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains. Issue 23 (1st December 2016)

• Record Type: Journal Article
• Authors: Shi, Zhiyan; Yang, Weiguo; Wang, Bei
• Is Part Of: Communications in statistics. Volume 45:Issue 23(2016)
• Page Start: 7027
• Page End: 7039
• Publication Date: 2016-12-01
• Subjects: Asymptotic circular Markov chains -- Asymptotic equipartition property (AEP) -- Small deviation theorem -- Strong law of large numbers (LLN).; 60F15 -- 60J10; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.972746
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In this article, we study a class of small deviation theorems for the random variables associated with m th-order asymptotic circular Markov chains. First, the definition of m th-order asymptotic circular Markov chain is introduced, then by applying the known results of the limit theorem for m th-order non homogeneous Markov chain, the small deviation theorem on the frequencies of occurrence of states for m th-order asymptotic circular Markov chains is established. Next, the strong law of large numbers and asymptotic equipartition property for this Markov chains are obtained. Finally, some results of m th-order nonhomogeneous Markov chains are given.