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Strong mixing coefficients for non-commutative Gaussian processes
Author(s):
Wlodzimierz
Bryc;
Victor
Kaftal
Journal:
Proc. Amer. Math. Soc.
132
(2004),
523-534.
MSC (2000):
Primary 81S05;
Secondary 60E99
Posted:
June 5, 2003
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Abstract:
Bounds for non-commutative versions of two classical strong mixing coefficients for  -Gaussian processes are found in terms of the angle between the underlying Hilbert spaces. As a consequence, we construct a  -mixing  -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:
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
Posted:
June 5, 2003
Communicated by:
David R. Larson
Copyright of article:
Copyright
2003,
American Mathematical Society
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