Abstract
Sufficient conditions for the applicability of the law of the iterated logarithm to sequences of dependent random variables are obtained. As a corollary, a theorem on the law of the iterated logarithm for a sequence of m-orthogonal random variables is proved.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Hoeffding and H. Robbins, “The central limit theorem for dependent random variables,” Duke Math. J. 15, 773–780 (1948).
V. V. Petrov, “Sequences of m-orthogonal random variables,” Zap. Nauchn. Semin. LOMI 119, 198–202 (1982) (in Russian); J. Soviet Math. 27 (1984), 3136–3140.
V. V. Petrov, “Law of the iterated logarithm for sequences of dependent random variables,” Zap. Nauchn. Semin. LOMI 97, 186–194 (1980) (in Russian); J. Soviet Math. 24 (1984), 611–617.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Petrov, 2017, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2017, Vol. 62, No. 1, pp. 48–52.
About this article
Cite this article
Petrov, V.V. On the law of the iterated logarithm for sequences of dependent random variables. Vestnik St.Petersb. Univ.Math. 50, 32–34 (2017). https://doi.org/10.3103/S1063454117010113
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1063454117010113