On the law of the iterated logarithm for weighted sums of independent random variables in a Banach space

• Date: 1993
• Main Authors: Matsak, I. K., Plichko, A. M., Мацак, І. К., Плічко, А. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1993
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/5924
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Assume that (X n) are independent random variables in a Banach space, (b n) is a sequence of real numbers, Sn= ∑ 1 n biXi, and Bn=∑ 1 n b i 2 . Under certain moment restrictions imposed on the variablesX n, the conditions for the growth of the sequence (bn) are established, which are sufficient fo...