Strong Laws of Large Numbers in an $$F^\alpha $$ F α -Scheme

Paul Doukhan (), Oleg I. Klesov () and Josef G. Steinebach ()
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Paul Doukhan: Université Cergy-Pontoise
Oleg I. Klesov: National Technical University of Ukraine (KPI), Department of Mathematical Analysis and Probability Theory
Josef G. Steinebach: Universität zu Köln, Mathematisches Institut

A chapter in Mathematical Statistics and Limit Theorems, 2015, pp 287-303 from Springer

Abstract: Abstract We study the almost sure limiting behavior of record times and the number of records, respectively, in a (so-called) $$F^\alpha $$ F α -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 Rényi (Annals Faculty Science University Clermont-Ferrand 8:7–12, 1962; Selected Papers of Alfred Rényi, vol. 3, pp. 50–65, Akadémiai Kiadó, Budapest 1976) for record times and counts.

Keywords: Number of records; Record times; $$F^\alpha $$ F α -scheme; Almost sure convergence; Strong law of large numbers (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12442-1_16

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DOI: 10.1007/978-3-319-12442-1_16

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