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

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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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1S 5B6, Canada

    Miklós Csörgő

  2. Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Zhishui Hu & Hongwei Mei

Authors
  1. Miklós Csörgő
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  2. Zhishui Hu
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  3. Hongwei Mei
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Corresponding author

Correspondence to Zhishui Hu.

Additional information

M. Csörgő research supported by an NSERC Canada Discovery Grant at Carleton University.

Z. Hu partially supported by NSFC (No. 10801122) and RFDP (No. 200803581009), and by an NSERC Canada Discovery Grant of M. Csörgő at Carleton University.

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Csörgő, M., Hu, Z. & Mei, H. Strassen-Type Law of the Iterated Logarithm for Self-normalized Sums. J Theor Probab 26, 311–328 (2013). https://doi.org/10.1007/s10959-011-0353-8

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  • DOI: https://doi.org/10.1007/s10959-011-0353-8

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