Sufficient conditions are obtained for the applicability of one of the classical forms of the law of iterated logarithm to a sequence of random variables without conditions of independence and the existence of any moments. Bibliography: 5 titles.
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V. V. Petrov, “On the law of the iterated logarithm without assumptions about the existence of moments,” Zap. Nauchn. Semin. POMI, 466, 208–210 (2017).
V. V. Petrov, “On the law of the iterated logarithm for a sequence of independent random variables with finite variances,” Zap. Nauchn. Semin. POMI, 278, 182–186 (2001).
H. Rubin and J. Sethuraman, “Probabilities of moderate deviations,” Sankhya, A27, No. 2–4, 325–346 (1965).
J. Sethuraman, “Probabilities of deviations,” in: Essays in probability and statistics, Univ. North Carolina Press, Chapel Hill (1970), pp. 655–672.
V. V. Petrov, “On probabilities of moderate deviations,” Zap. Nauchn. Semin. POMI, 260, 214–217 (1999).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 474, 2018, pp. 195–198.
Translated by I. Ponomarenko.
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Petrov, V.V. The Law of the Iterated Logarithm and Probabilities of Moderate Deviations of Sums of Dependent Random Variables. J Math Sci 251, 128–130 (2020). https://doi.org/10.1007/s10958-020-05072-w
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DOI: https://doi.org/10.1007/s10958-020-05072-w