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Strong Limit Properties for Generalized Non-Symmetric Markov Chain Fields on Trees

Author: SongYuQin
Tutor: YangWeiGuo
School: Jiangsu University
Course: Applied Mathematics
Keywords: Tree With the airport The asymmetric tree Markov chains field Martingale State ordered pair Strong Law of Large Numbers Shannon-McMillan theorem
CLC: O211.6
Type: Master's thesis
Year: 2006
Downloads: 17
Quote: 0
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Abstract


The tree with the airport is the theory of stochastic processes in the the tree a mathematical model of the application , it is produced in the encoding and decoding of information theory . Suppose a sequence { X_n } , which the state and the state ordered pair frequency whether to comply with the law of large numbers , a direct impact on the pros and cons of the encoding and decoding method , so this area has been the focus of many scholars . Thirty years ago, the birth of the \With the development of information theory , the tree graph model in recent years caused by physics , probability theory and information theory community wide interest , information theory, Shannon-McMillan theorem also became a hot research scholars . Recently , Yang Weiguo and his collaborators use of new methods of study probability theory limit theorem traditional Markov chain Some Strong Limit Theorem , Shannon-McMillan theorem to the Bethe tree and Markov chain fields on Cayley trees . Nonhomogeneous Markov chain field , only the odd Markov chain fields perfect . This article is mainly on the the generalized asymmetric limit theory of Markov chains field of research . First define a tree generalized asymmetric Markov chain fields using the martingale method constructed martingale , Doob martingale convergence theorem and some special inequalities research tree generalized non - symmetrical 's chain field strength limit theorem , the tree generalized local convergence theorem for symmetric Markov chain field and on the state and the state ordered pair frequency powerful theorem ae convergence of the Shannon-McMillan theorem .

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Theory of probability ( probability theory, probability theory ) > Random process
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