Acta mathematica scientia,Series A

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The Markov Approximation of the Random Fields on Cayley Trees and a Class of Small Deviation Theorems

 LIU Wen, WANG Li-Ying   

  1. 河北工业大学应用数学研究所 天津 300130 

    石家庄铁道学院基础部 石家庄 050043
  • Online:2003-06-25 Published:2003-06-25
  • Supported by:

    国家自然科学基金资助项目(19871022)

Abstract:

 By introducing the sample relative entropy rate as a measure of the deviation bewteen 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  are established. In the proof a new analytic technique in the study of the strong limit theorems for Markov chains is applied.

Key words:  Markov chain fields on Cayley trees, Sample relative entropy rate, Small deviation theorem, Strong deviation theorem, Strong limit theorem

CLC Number: 

  • 60F15
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