A limit theorem related to the Hartman–Wintner–Strassen LIL and the Chover LIL

Deli Li and Shuhua Zhang

Statistics & Probability Letters, 2016, vol. 109, issue C, 16-21

Abstract: Let {X,Xn;n≥1} be a sequence of i.i.d. real-valued random variables, and let Sn=∑i=1nXi,n≥1. Write logx=loge(e∨x), x≥0. In this note we establish a limit theorem which is related to the classical Hartman–Wintner–Strassen law of the iterated logarithm and the classical Chover law of the iterated logarithm. That is, for 1≤p<∞, we show that lim supn→∞|Snn|(logloglogn)−1=ep/2almost surely if and only if EX=0andinf{b>0:limx→∞(loglogx)1−bE(X2I(|X|≤x))=0}=p.

Keywords: Chover law of the iterated logarithm; Hartman–Wintner–Strassen law of the iterated logarithm; Sums of i.i.d. random variables (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spl.2015.10.007

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