Convergence rates for weighted sums in noncommutative probability space |
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| Authors: | Byoung Jin Choi Un Cig Ji |
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| Institution: | 1. Department of Mathematics, Chungbuk National University, Cheongju 361-763, Republic of Korea;2. Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Republic of Korea |
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| Abstract: | We study convergence rates for weighted sums of pairwise independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. As applications, we first study convergence rates for weighted sums of random variables in the noncommutative Lorentz space, and second we study convergence rates for weighted sums of probability measures with respect to the free additive convolution. |
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| Keywords: | Noncommutative probability space Weighted sum Weak law of large numbers Convergence rate Noncommutative Lorentz space Free convolution |
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