Exponential convergence rates for weighted sums in noncommutative probability space
2016 ◽
Vol 19
(04)
◽
pp. 1650027
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Keyword(s):
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.
2014 ◽
Vol 409
(2)
◽
pp. 963-972
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2012 ◽
Vol 05
(01)
◽
pp. 1250007
1969 ◽
Vol 20
(2)
◽
pp. 570-570
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Keyword(s):
2020 ◽
pp. 89-93
1991 ◽
Vol 14
(2)
◽
pp. 381-384
Keyword(s):
2008 ◽
Vol 337
(2)
◽
pp. 1226-1237
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Keyword(s):