Title: New and old results on strong approximations.
In this talk we first give a survey of previous work on
optimal strong invariance principles for sums of iid random variables.
In the 1-dimensional case the strong approximation problem has
essentially been solved in 1976 by Komlos-Major-Tusnady. Comparable
results in the multivariate setting habe been established much later.
Most of these results require at least finite second moments and in the
second part of the talk we will present a new result in the infinite
variance case and show how it can be used to generalize Strassen's
(1964) functional LIL.
