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

 

Weak ergodicity of stationary pairwise independent processes


Authors: D. Landers and L. Rogge
Journal: Proc. Amer. Math. Soc. 128 (2000), 1203-1206
MSC (1991): Primary 60G10; Secondary 60F20
Published electronically: July 28, 1999
MathSciNet review: 1654085
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Abstract: It is proven that a stationary process of pairwise independent random variables with values in a separable metric space is weakly ergodic, i.e. each random variable is independent of the system of invariant sets of the process. An example shows that a process of identically distributed pairwise independent random variables is in general, however, not weakly ergodic.


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Additional Information

D. Landers
Affiliation: Mathematisches Institut der Universität zu Köln, Weyertal 86, D–50931 Köln, Germany
Email: landers@mi.uni-koeln.de

L. Rogge
Affiliation: Fachbereich Mathematik der Gerhard-Mercator-Universität ghs Duisburg, Lotharstr. 65, D–47048 Duisburg, Germany
Email: rogge@math.uni-duisburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05249-1
PII: S 0002-9939(99)05249-1
Keywords: Stationary processes, pairwise independent random variables, ergodicity
Received by editor(s): May 19, 1998
Published electronically: July 28, 1999
Communicated by: James Glimm
Article copyright: © Copyright 2000 American Mathematical Society