Abstract
We establish a noncommutative extension of the Fuk–Nagaev inequalities for random variables in a noncommutative probability space. As applications, we first obtain noncommutative versions of Bennett inequality and Rosenthal inequality, and secondly, we study the weak law of large numbers for weighted sums in a noncommutative probability space and the weak law of large numbers for weighted sums of probability measures corresponding to the free additive convolutions.
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Communicated by Mohammad Sal Moslehian.
UCJ was supported by Basic Science Research Program through the NRF funded by the MEST (No. NRF-2013R1A1A2013712).
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Choi, B.J., Ji, U.C. Noncommutative Fuk–Nagaev Inequalities and Their Applications. Bull. Malays. Math. Sci. Soc. 41, 1327–1342 (2018). https://doi.org/10.1007/s40840-016-0394-3
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DOI: https://doi.org/10.1007/s40840-016-0394-3
Keywords
- Noncommutative probability space
- Fuk–Nagaev inequality
- Bennett inequality
- Rosenthal inequality
- Weak law of large numbers
- Free convolution