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))
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.