Sufficient conditions are found for the applicability of the generalized law of the iterated logarithm for sums of random variables without conditions of independence and existence of moments.
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A. Kolmogoroff, “¨Uber das Gesetz des iterierten Logarithmus,” Math. Ann., 101, 126–135 (1929).
V. V. Petrov, Limit Theorems of Probability Theory, Oxford Univ. Press, New York (1995).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 466, 2017, pp. 208–211.
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Petrov, V.V. On the Law of the Iterated Logarithm Without Assumptions About the Existence of Moments. J Math Sci 244, 840–841 (2020). https://doi.org/10.1007/s10958-020-04656-w
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DOI: https://doi.org/10.1007/s10958-020-04656-w