Abstract
In the paper, a sharpened version of a theorem of W. Feller on the law of iterated logarithms is proved. Bibliography: 5 titles.
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References
W. Feller, “On the oscillations of identically distributed random variables,”Ann. Math.,91, No. 2, 402–418 (1970).
W. Feller, “An extension of the law of iterated logarithms to variables without variance,”J. Math. Mech.,18, No. 4, 345–355 (1968).
V. V. Petrov,Limit Theorems for Sums of Independent Random Variables [in Russian], Nauka, Moscow (1987).
A. I. Martikainen and V. V. Petrov, “On the necessary and sufficient conditions for the law of iterated logarithms,”Teor. Veroyatn. Primenen.,22, No. 1, 18–26 (1977).
L. V. Rozovsky, “Estimates for probabilities of one-sided large deviations,”Teor. Veroyatn. Primenen.,30, No. 4, 800–804 (1985).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 117–123.
Translated by the author.
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Rozovsky, L.V. Pharpening of a feller theorem on the law of iterated logarithms. J Math Sci 88, 81–85 (1998). https://doi.org/10.1007/BF02363266
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DOI: https://doi.org/10.1007/BF02363266