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One moment estimate for the supremum of normalized sums in the law of the iterated logarithm

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Abstract

For a sequence of independent random elements in a Banach space, we obtain an upper bound for moments of the supremum of normalized sums in the law of the iterated logarithm by using an estimate for moments in the law of large numbers. An example of their application to the law of the iterated logarithm in Banach lattices is given.

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Authors and Affiliations

  1. Kyiv National University of Technology and Design, Kyiv

    I. K. Matsak

  2. Kirovohrad Pedagogic University, Kirovohrad

    A. M. Plichko

Authors
  1. I. K. Matsak
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  2. A. M. Plichko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 5, pp. 653–665, May, 2006.

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Matsak, I.K., Plichko, A.M. One moment estimate for the supremum of normalized sums in the law of the iterated logarithm. Ukr Math J 58, 737–750 (2006). https://doi.org/10.1007/s11253-006-0098-1

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  • DOI: https://doi.org/10.1007/s11253-006-0098-1

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