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一类非齐次树上关于马氏链场滑动平均的强偏差定理

A Strong Deviation Theorem for the Moving Averages of Markov Chain Fields on a Non-homogenous Tree
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摘要 树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.本文利用Borel-Cantelli引理研究给出了一类非齐次树上马氏链场关于负二项分布滑动平均的强偏差定理. In recent years, tree indexed stochastic process has become one of the hot topics in probability theory. The deviation theorem has been one of the central issues of the international probability theory. In this paper, by means of Borel-Cantelli lemma, a strong deviation theorem for the moving averages of Markov chain fields on a non-homogenous tree is given.
出处 《大学数学》 2015年第4期25-29,共5页 College Mathematics
基金 河北省高等学校科学技术重点研究项目(ZD2014051)
关键词 非齐次树 负二项分布 马氏链 强偏差定理 non-homogeneous tree negative binomial distribution Markov chain strong deviation theorem
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参考文献2

  • 1Shi Z Y, Yang W G. Some limit properties for the m-th-order non-homogeneous Markov chains indexed by an m rooted Cayley tree[J]. Statist Prohab Lett, 2010, 80(15): 1223-1233.
  • 2Yang W G: A class of deviation theorems for the random fields associated with non-homogeneous Markov chains indexed by a Bethe tree[J]. Stochastic Analysis and Applications, 2012, 30(2):220-237.

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