Abstract
We obtain some results concerning the upper limit of a random sequence and the law of the iterated logarithm for sums of independent random variables.
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REFERENCES
V. V. Petrov, “Some estimates for sums of dependent random variables that are satisfied almost surely,” Zap. Nauchn. Semin. Leningrad. Otdelen. Mat. Inst. Akad. Nauk SSSR, 55, 113–116 (1976).
V. V. Petrov, “On the law of the iterated logarithm for sequences of dependent random variables,” Zap. Nauchn. Semin. Leningrad. Otdelen. Mat. Inst. Akad. Nauk SSSR, 97, 186–194 (1980).
V. V. Petrov, “On the relationship between the estimate of the residual term in the central limit theorem and the law of the iterated logarithm,” Teor. Ver. Primen., 11, No.3, 514–518 (1966).
V. V. Petrov, “One theorem on the law of the iterated logarithm,” Teor. Ver. Primen., 16, No.4, 715–718 (1971).
V. V. Petrov, Limit Theorems of Probability Theory, Oxford University Press, Oxford (1995).
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Petrov, V.V. On the Upper Limit of a Random Sequence and the Law of the Iterated Logarithm. Ukrainian Mathematical Journal 52, 1453–1456 (2000). https://doi.org/10.1023/A:1010336304178
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DOI: https://doi.org/10.1023/A:1010336304178