Bounded law of the iterated logarithm for multidimensional martingales normalized by matrices

  • V. A. Koval

Abstract

We investigate a bounded law of the iterated logarithm for matrix-normalized weighted sums of martingale differences in $R^d$. We consider the normalization of matrices inverse to the covariance matrices of these sums by square roots. This result is used for the proof of the bounded law of the iterated logarithm for martingales with arbitrary matrix normalization.
Published
25.07.2006
How to Cite
Koval, V. A. “Bounded Law of the Iterated Logarithm for Multidimensional Martingales Normalized by Matrices”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 7, July 2006, pp. 1006–1008, https://umj.imath.kiev.ua/index.php/umj/article/view/3510.
Section
Short communications