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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong mixing coefficients for non-commutative Gaussian processes


Authors: Wlodzimierz Bryc and Victor Kaftal
Journal: Proc. Amer. Math. Soc. 132 (2004), 523-534
MSC (2000): Primary 81S05; Secondary 60E99
Published electronically: June 5, 2003
MathSciNet review: 2022378
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Abstract: Bounds for non-commutative versions of two classical strong mixing coefficients for $q$-Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a $\psi$-mixing $q$-Gaussian stationary sequence with growth conditions on variances of partial sums. If classical processes with analogous properties were to exist, they would provide a counter-example to the Ibragimov conjecture.


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Additional Information

Wlodzimierz Bryc
Affiliation: Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221–0025
Email: Wlodzimierz.Bryc@UC.edu

Victor Kaftal
Affiliation: Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221–0025
Email: Victor.Kaftal@UC.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07051-5
PII: S 0002-9939(03)07051-5
Keywords: Non-commutative uniform strong mixing, Ibragimov's conjecture, covariance estimates
Received by editor(s): September 12, 2002
Published electronically: June 5, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society