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

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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