Journal of Soviet Mathematics

, Volume 20, Issue 3, pp 2214–2221 | Cite as

An exponential criterion for the law of the iterated logarithm

  • A. I. Martikainen
Article

Abstract

Necessary and sufficient conditions are found for relations of the type of the law of the iterated logarithm expressed in terms of “exponential moments” of independent terms.

Keywords

Iterate Logarithm Independent Term Exponential Moment Exponential Criterion 
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Literature cited

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    A. I. Martikainen and V. V. Petrov, “On necessary and sufficient conditions for the law of the iterated logarithm,” Teor. Veroyatn. Primen.,22, No. 1, 18–26 (1977);22, No. 2, 442 (1977).Google Scholar
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    S. D. Chatterjee and R. P. Pakshirajan, “On the unboundedness of infinitely divisible laws,” Sankhya,17, No. 4, 349–350 (1955).Google Scholar
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    A. I. Martikainen, “On the limit superior of sums of independent random variables,” Theses of the Second Vilnius Conference on Probability Theory and Mathematical Statistics, Vol. 2, Vilnius (1977), pp. 15–16.Google Scholar
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    M. S. Klass, “On stopping rules and expected supremum of Sn/a n and ¦Sn¦/a n,” Ann. Probab.,2, No. 5, 889–905 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • A. I. Martikainen

There are no affiliations available

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