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Generalizations of KMT Approximation for partial sums of non-i.i.d. random variables
发布时间: 2018-05-08     19:19   【返回上一页】 发布人:Alexander Sakhanenko


随机数学中心学术报告

 

题目: Generalizations of KMT Approximation for partial sums of non-i.i.d. random variables

 

报告人Alexander Sakhanenko (Sobolev Institute of Mathematics, Novosibirsk (RUSSIA))

 

邀请人: 洪文明

 

时间2018 年5月15日(星期二)下午2:00-3:00

 

地点后主楼1220B

 

摘要: The famouse approximation theorems due to J.Komlos, P.Major and G.Tusmady are powerful tool in many investigations where we want to obtain asymptotical distributions of complicated functionals dependent on a path of some random walk. In the talk all these results will be reviewed in a compact form to show all their advantages and disadvantages. For example, KMT approximations hold only for i.i.d. random variables with implicit dependence on their common distribution. After that a new estimate due to the author will be presented.  It alone implies all KMT approximations and depend in explicit way on all used parameters of the common distribution. Moreover, several more general results for sequences of sums of non-identically distributed independent random variables will be presented. They also depend explicitly on all used parameters of distributions. The latter allows us to apply these estimates also in the case of double arrays of random variables, the case which is essential in many modern statistical problems. Note also that all presented estimates of the author are unimprovable up to some absolute constants.