A universal result in almost sure central limit theory.
The paper presents results generalizing the almost sure central limit theorem in several ways. The weights in formula are relaxed, the considered functions of observations are allowed general such that sum and/or maximum became examples, only, and an arbitrary distribution function can serve as the limit instead of Gaussian one. The paper finishes with interesting consequences for random walks, U-statistics, Kolmogorov-Smirnov statistics, etc.
scientific article; zbMATH DE number 2119510
scientific article