Abstract
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.
Citation
Ali Talebi. Mohammad Sal Moslehian. Ghadir Sadeghi. "Etemadi and Kolmogorov Inequalities in Noncommutative Probability Spaces." Michigan Math. J. 68 (1) 57 - 69, April 2019. https://doi.org/10.1307/mmj/1541667627
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