The Michigan Mathematical Journal
- Michigan Math. J.
- Volume 68, Issue 1 (2019), 57-69.
Etemadi and Kolmogorov Inequalities in Noncommutative Probability Spaces
Based on a maximal inequality-type result of Cuculescu, we establish some noncommutative maximal inequalities such as the Hajék–Penyi and Etemadi inequalities. In addition, we present a noncommutative Kolmogorov-type inequality by showing that if are successively independent self-adjoint random variables in a noncommutative probability space such that and , where , then, for any , there exists a projection such that
As a result, we investigate the relation between the convergence of a series of independent random variables and the corresponding series of their variances.
Michigan Math. J., Volume 68, Issue 1 (2019), 57-69.
Received: 1 February 2017
Revised: 25 September 2017
First available in Project Euclid: 8 November 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Primary: 46L53: Noncommutative probability and statistics
Secondary: 46L10: General theory of von Neumann algebras 47A30: Norms (inequalities, more than one norm, etc.) 60F99: None of the above, but in this section
Talebi, Ali; Moslehian, Mohammad Sal; Sadeghi, Ghadir. Etemadi and Kolmogorov Inequalities in Noncommutative Probability Spaces. Michigan Math. J. 68 (2019), no. 1, 57--69. doi:10.1307/mmj/1541667627. https://projecteuclid.org/euclid.mmj/1541667627