Strassen-Type Law of the Iterated Logarithm for Self-normalized Sums

Miklós Csörgő (), Zhishui Hu () and Hongwei Mei ()
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Miklós Csörgő: Carleton University
Zhishui Hu: University of Science and Technology of China
Hongwei Mei: University of Science and Technology of China

Journal of Theoretical Probability, 2013, vol. 26, issue 2, 311-328

Abstract: Abstract Let {X,X n ,n≥1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX 2 I(|X|≤x) is slowly varying as x→∞. In this paper it is shown that a Strassen-type law of the iterated logarithm holds for self-normalized sums of such random variables, i.e., when X is in the domain of attraction of the normal law.

Keywords: Strassen-type law of the iterated logarithm; Self-normalized sums; Domain of attraction of the normal law; 60F15; 60G50 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10959-011-0353-8

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