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.
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Literature cited
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).
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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.
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).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 85, pp. 158–168, 1979.
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Martikainen, A.I. An exponential criterion for the law of the iterated logarithm. J Math Sci 20, 2214–2221 (1982). https://doi.org/10.1007/BF01239999
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DOI: https://doi.org/10.1007/BF01239999