Doukhan, Paul; Klesov, Oleg I.; Steinebach, Josef G. Strong laws of large numbers in an \(F^{\alpha}\)-scheme. (English) Zbl 1378.60059 Hallin, Marc (ed.) et al., Mathematical statistics and limit theorems. Festschrift in honour of Paul Deheuvels. Selected papers based on the presentations at the conference on the occasion of his 65th birthday, Paris, France, June 20–21, 2013. Cham: Springer (ISBN 978-3-319-12441-4/hbk; 978-3-319-12442-1/ebook). 287-303 (2015). Summary: We study the almost sure limiting behavior of record times and the number of records, respectively, in a (so-called) \(F^{\alpha}\)-scheme. It turns out that there are certain “dualities” between the latter results, that is, under rather general conditions strong laws for record times can be derived from the corresponding ones for the number of records, but in general not vice versa. The results extend, for example, the classical strong laws of A. Rényi [in: Colloquium on combinatorial methods in probability theory, August 1–10, 1962. Lectures. Aarhus: Matematisk Institut, Aarhus Universitet. 104–115 (1962; Zbl 0139.35303); “On the extreme elements of observations”, in: Selected Papers of Alfred Rényi 3. Budapest: Akadémiai Kiadó. 50–65 (1976)] for record times and counts.For the entire collection see [Zbl 1316.60007]. Cited in 1 Document MSC: 60F15 Strong limit theorems Keywords:number of records; record times; \(F^{\alpha}\) scheme; almost sure convergence; strong law of large numbers Citations:Zbl 0139.35303 PDFBibTeX XMLCite \textit{P. Doukhan} et al., in: Mathematical statistics and limit theorems. Festschrift in honour of Paul Deheuvels. Selected papers based on the presentations at the conference on the occasion of his 65th birthday, Paris, France, June 20--21, 2013. Cham: Springer. 287--303 (2015; Zbl 1378.60059) Full Text: DOI