| The law of the iterated logarithm is a kind of profound results in probability limit theory and the accuracy of strong law of large numbers,the most famous conclusion in independent identically distributed case is the law of the iterated logarithm due to Hartman-Wintner.Lots of home and abroad mathematical statisticians have studied many properties related to the above conclusion.The rate of convergence of the law of iterated logarithm is widely used in many fields such as the probability limit theory.In the course of development,the famous conclusion that researchers got is the Davis-Gut law.But in practical examples of real life,the samples are ofen not independent of each other.Thus,in recent years,research on the concepts and properties of mixing random variables gradually aroused widespread concern.Then there have been m-dependent sequence,?-mixing sequence,?-mixing sequence and NA sequence and so on.In this paper,we mainly study the Davis-Gut law in the case of m-dependent sequence and ?-mixing sequence.This paper has three chapters,the first chapter introduce the background and development of the law of iterated logarithm due to Hartman-Wintner and its convergence rate.In the second chapter,we obtain the conclusion of Davis-Gut law in the m-dependent case.The third chapter obtains the conclusion of Davis-Gut law in the ?-mixing case. |
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