We consider partial sums of i.i.d. random variables with moments E(X1)=0, E(X12)=[sigma]2 and and show thatwith some explicit function [phi](·). A related result for random variables with exponentially thin tails has recently been shown by Steinebach, extending a result given by Shao.

We discuss almost sure versions of distributional limit theorems for central and intermediate order statistics.

We prove an almost sure version of a maximum limit theorem using logarithmic means and show that essentially only logarithmic means work as it is the case for almost sure central limit theorems.

We consider the problem of estimating a class of smooth functions defined everywhere on a real line utilizing nonparametric kernel regression estimators. Such functions have an interpretation as signals and are common in communication theory. Furthermore, they have finite energy, bounded...

We consider weighted sums with iid random variables (Xn) and compare the tail probabilities of these sums with the moment conditions on X1. If X1 is in the domain of attraction of a stable law then refined Baum-Katz laws generalizing results of Heyde, Gut and other authors are presented. Some...