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Functional Erdős-Rényi laws. (English) Zbl 0767.60029

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.

MSC:

60F15 Strong limit theorems
60F10 Large deviations
60F17 Functional limit theorems; invariance principles
60G50 Sums of independent random variables; random walks

Citations:

Zbl 0225.60015
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