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
DOI:
https://doi.org/10.1090/S0002-9939-99-05249-1
Published electronically:
July 28, 1999
MathSciNet review:
1654085
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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:
https://doi.org/10.1090/S0002-9939-99-05249-1
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
