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| 摘要: |
| 本文研究了二叉树指标随机场关于分枝马氏链的一类强偏差定理.通过引入渐近对数似然比作为二叉树指标任意随机场与分枝马氏链之间偏差的一种度量，进而构造鞅的方法，获得了二叉树指标随机场关于分枝马氏链的一类强偏差定理，推广得到了二叉树指标分枝马氏链的强大数定理和渐近均分性. |
| 关键词: 二叉树 分枝马氏链 强偏差定理 渐近均分性 强大数定律 |
| DOI： |
| 分类号:O211.6 |
| 基金项目:国家自然科学基金资助（11571142）. |
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| A CLASS OF STRONG DEVIATION THEOREMS FOR THE RANDOM FIELDS ASSOCIATED WITH BIFURCATING MARKOV CHAINS INDEXED BY A BINARY TREE |
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MIN Fan,YANG Wei-Guo
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| Abstract: |
| In this paper, we study a class of strong deviation theorems for the random fields which are associated with bifurcating Markov chains indexed by a binary tree. By introducing the asymptotic logarithmic likelihood ratio as a measure of the deviation between the arbitrary random fields and the bifurcating Markov chains on a binary tree, and constructing the martingale, a class of strong deviation theorems for the random fields which are associated with bifurcating Markov chains indexed by a binary tree is established. As corollaries, we obtain the strong law of large numbers and the AEP for the bifurcating Markov chains indexed by a binary tree. |
| Key words: binary tree bifurcating Markov chains strong deviation theorem asymptotic equipartition property strong law of large numbers |
