Adler, André A note on the almost sure limiting behavior of the maximum of a sequence of partial sums. (English) Zbl 0691.60024 Stochastica 12, No. 2-3, 235-240 (1988). Summary: The goal of this paper is to show that, in most strong laws of large numbers, the n th partial sum can be replaced with the largest of the first n sums. Moreover, it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results also apply to strong laws for Banach valued random elements. MSC: 60F15 Strong limit theorems 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) Keywords:maximum of a sequence of partial sums; strong laws of large numbers; strong laws for Banach valued random elements PDFBibTeX XMLCite \textit{A. Adler}, Stochastica 12, No. 2--3, 235--240 (1988; Zbl 0691.60024) Full Text: EuDML