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A class of mixed random sequence of probability limit theorems

Author: ChaZuoZuo
Tutor: HuShuHe
School: Anhui University
Course: Probability Theory and Mathematical Statistics
Keywords: PA sequence  ~ ) Mixed Strong positive dependence Strong Law Convergence rate
CLC: O211
Type: Master's thesis
Year: 2007
Downloads: 108
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Abstract


Probability theory is to describe the significance of the large number of random factors demonstrated by the regularity Therefore, the study limits for random variables and random nature of the phenomenon has a clear and important value. Mutually independent random variables on the probability limit theory, the early 20th century, four decades has gained considerable improvement in terms of its basic results are summarized in Gnedenko and Kolmogorov's monograph \[25]) in. However, in many practical problems, the sample is not a separate or independent samples of some of the functions are not independent; the other hand, theoretical studies and other subjects appear in the branch has a dependency on the variable requirements, such as the Markov chain, with the Airport theories and issues such as time series analysis. Thus, by the mid 1950s, following the independent random variables and the development of a complete theory of the classical limit, the random variable dependencies concept of probability theory and mathematical statistics in some branches have been proposed, and caused a lot probability statistics family's interest and research, thus made a lot of research, which until 1997 included many results are summarized in METROLOGY Lin Cheng Yan monograph \Probability theory is the central research topics Strong laws, and discuss the strong law of large numbers and convergence rate occupies a very important position. Usually prove strong law, there are two basic methods, the first method is to first prove a subsequence sequence Strong Law of obedience, then this conclusion to the entire sequence, this method is called sub-sequences, in which part and the need to use the maximum value of inequality; second method is through Hájek ~ Rényi type maxima inequality proved that due to Hájek-Rényi type inequality maxima card was not easy, so the sub-sequence method is more commonly used, however, Once you get the maximum value Hájek-Rényi type inequality, Strong evidence on the change is obvious. Fazekas and Klesov in 2000 in the literature [2] to establish a maximum value Hájek-Rényi type inequalities, and to promote the use of its dependent random variables and on the relevant conclusions, thus using the second method is more convenient to discuss . Full divided into three chapters, the first chapter introduces random variables related to some of the concepts, definitions, symbols, conclusions are given the required inequality, lemma and the corresponding number of inferences; Chapter lemma using the first chapter and inferential , obtained under certain conditions, a mean of 0 and a part of the PA sequence Almost everywhere convergence, strong law of large numbers and convergence rate for such conclusions; Chapter PA serial correlation in contrast to conclusions on the basis of further study strongly positive random variables sequence (?) mixing sequences, etc. in case of strong law of large numbers and convergence rate.

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