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October, 1975 Coefficient Properties of Random Variable Sequences
William J. Barlow
Ann. Probab. 3(5): 840-848 (October, 1975). DOI: 10.1214/aop/1176996270


Burkholder [3] gave a simple necessary and sufficient condition, in terms of concentration functions, for independent sequences of random variables to have the Stein property. Here we find sufficient conditions for the Stein property without assuming that the random variable sequence is independent. Our conditions are also in terms of concentration functions, but in our case they are conditional concentration functions which specialize to those used by Burkholder. For some of our results, the sequence of random variables may be quite arbitrary; however, we usually assume it to be a martingale difference sequence satisfying certain regularity conditions.


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William J. Barlow. "Coefficient Properties of Random Variable Sequences." Ann. Probab. 3 (5) 840 - 848, October, 1975.


Published: October, 1975
First available in Project Euclid: 19 April 2007

zbMATH: 0317.60021
MathSciNet: MR388530
Digital Object Identifier: 10.1214/aop/1176996270

Primary: 60G45
Secondary: 60G50

Keywords: conditional concentration function , martingale , Stein property

Rights: Copyright © 1975 Institute of Mathematical Statistics


Vol.3 • No. 5 • October, 1975
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