Abstract
One proves two theorems on the law of the iterated logarithm for sequences of random variables that are not necessarily independent. These theorems are the one-sided analogues of certain results of Lai and Stout.
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Literature cited
T. L. Lai and W. Stout, “Limit theorems for sums of dependent random variables,” Z. Wahrsch. Verw. Gebiete,51, No. 1, 1–14 (1980).
V. V. Petrov, “On the law of iterated logarithm for sequences of dependent random variables,” J. Sov. Math.,24, No. 5 (1984).
T. L. Lai and W. Stout, “The law of the iterated logarithm and upper-lower class tests for partial sums of stationary Gaussian sequences,” Ann. Probab.,6, No. 5, 731–750 (1978).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Institua im. V. A. Steklova AN SSSR, Vol. 130, pp. 150–156, 1983.
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Petrov, V.V. One-sided theorems on the law of the iterated logarithm without the independence assumption. J Math Sci 27, 3274–3278 (1984). https://doi.org/10.1007/BF01850677
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DOI: https://doi.org/10.1007/BF01850677