We obtain asymptotic estimates in the law of iterated logarithm for the extreme values of a sequence of independent random variables in Banach spaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
L. de Haan and A. Hordijk, “The rate of growth of sample maxima,” Ann. Math. Statist., 43, 1185–1196 (1972).
J. Pickands, “Sample sequences of maxima,” Ann. Math. Statist., 38, No. 5, 1570–1574 (1967).
K. S. Akbash and I. K. Matsak, “One improvement of the law of the iterated logarithm for the maximum scheme,” Ukr. Mat. Zh., 64, No. 8, 1132–1137 (2012); English translation:Ukr. Math. J., 64, No. 8, 1290–1296 (2013).
R. von Mises, “La distribution de la plus grande de n valeurs,” in: Selected Papers II, American Mathematical Society (1936), pp. 271–294.
J. Lindenstraus and L. Tzafriri, Classical Banach Spaces, Vol. 2, Springer, Berlin (1979).
K. S. Akbash, “Exponential estimates for the maximum scheme,” Ukr. Mat. Zh., 69, No. 7, 984–991 (2017); English translation:Ukr. Math. J., 69, No. 7, 1144–1153 (2017).
L. V. Kantorovich and G. P. Akilov, Functional Analysis [in Russian], Nauka, Moscow (1984).
Ya. I. Galambosh, Asymptotic Theory of Extremal Order Statistics [in Russian], Nauka, Moscow (1984).
I. K. Matsak and A. M. Plichko, “On the maxima of independent random elements in a functional Banach lattice” Teor. Imovirn. Mat. Statyst., Issue 61, 105–116 (1999).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 3, pp. 303–309, March, 2019.
Rights and permissions
About this article
Cite this article
Akbash, K.S., Makarchuk, O.P. On the Law of Iterated Logarithm for the Maximum Scheme in Ideal Banach Spaces. Ukr Math J 71, 343–351 (2019). https://doi.org/10.1007/s11253-019-01650-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-019-01650-7