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

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  • Liu, Wen
  • Wang, Liying

Abstract

By introducing the sample relative entropy rate as a measure of the deviation between the arbitrary random fields and the Markov chain fields 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.

Suggested Citation

  • Liu, Wen & Wang, Liying, 2003. "The Markov approximation of the random fields on Cayley trees and a class of small deviation theorems," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 113-121, June.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:2:p:113-121
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    References listed on IDEAS

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    1. Liu, Wen & Yang, Weiguo, 2000. "The Markov approximation of the sequences of N-valued random variables and a class of small deviation theorems," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 117-130, September.
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