The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems

✍ Scribed by Wen Liu; Liying Wang

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 220 KB
• Volume: 63
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(03)00058-0

✦ Synopsis

By introducing the sample relative entropy rate as a measure of the deviation between the arbitrary random ÿelds and the Markov chain ÿelds on Cayley trees, a class of small deviation theorems for the frequencies of state ordered couples is established. In the proof a new analytic technique in the study of the strong limit theorems for Markov chains is applied.