Deheuvels, Paul Functional Erdős-Rényi laws. (English) Zbl 0767.60029 Stud. Sci. Math. Hung. 26, No. 2-3, 261-295 (1991). Main purpose of this paper is to establish a functional version of the Erdős-Rényi law of large numbers [P. Erdős and A. Rényi, J. Anal. Math. 23, 103-111 (1970; Zbl 0225.60015)] concerning increments of partial sum processes over subintervals of critical length \(a_ T\sim c\log T\) \((T\to\infty)\). A number of preliminary results on large deviations, Chernoff functions and functional spaces are also presented being of independent interest. The paper closes by discussing possible applications and relations to corresponding problems in other settings. Reviewer: J.Steinebach (Marburg) Cited in 1 ReviewCited in 12 Documents MSC: 60F15 Strong limit theorems 60F10 Large deviations 60F17 Functional limit theorems; invariance principles 60G50 Sums of independent random variables; random walks Keywords:functional laws; Erdős-Rényi law; strong law; law of the iterated logarithm; law of large numbers; increments of partial sum processes; large deviations Citations:Zbl 0225.60015 PDFBibTeX XMLCite \textit{P. Deheuvels}, Stud. Sci. Math. Hung. 26, No. 2--3, 261--295 (1991; Zbl 0767.60029)