2019
Том 71
№ 11

One moment estimate for the supremum of normalized sums in the law of the iterated logarithm

Abstract

For a sequence of independent random elements in a Banach space, we obtain an upper bound for moments of the supremum of normalized sums in the law of the iterated logarithm by using an estimate for moments in the law of large numbers. An example of their application to the law of the iterated logarithm in Banach lattices is given.

English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 5, pp 737-750.

Citation Example: Matsak I. K., Plichko A. M. One moment estimate for the supremum of normalized sums in the law of the iterated logarithm // Ukr. Mat. Zh. - 2006. - 58, № 5. - pp. 653–665.

Full text