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- Title
Exponential convergence rates for weighted sums in noncommutative probability space.
- Authors
Choi, Byoung Jin; Ji, Un Cig
- Abstract
We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.
- Subjects
STOCHASTIC convergence; PROBABILITY theory; NONCOMMUTATIVE algebras; TOPOLOGY; RING extensions (Algebra)
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2016, Vol 19, Issue 4, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025716500272