A class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains

作者：Shi, Zhiyan^*; Yang, Weiguo; Wang, Bei

来源：Communications in Statistics - Theory and Methods, 2016, 45(23): 7027-7039.

DOI：10.1080/03610926.2014.972746

• Asymptotic circular Markov chains
• Asymptotic equipartition property (AEP)
• Small deviation theorem
• Strong law of large numbers (LLN)

In this article, we study a class of small deviation theorems for the random variables associated with mth-order asymptotic circular Markov chains. First, the definition of mth-order asymptotic circular Markov chain is introduced, then by applying the known results of the limit theorem for mth-order non homogeneous Markov chain, the small deviation theorem on the frequencies of occurrence of states for mth-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 mth-order nonhomogeneous Markov chains are given.

• 出版日期2016
• 单位江苏大学