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Weak ergodicity of stationary pairwise independent processes
Author(s):
D.
Landers;
L.
Rogge
Journal:
Proc. Amer. Math. Soc.
128
(2000),
1203-1206.
MSC (1991):
Primary 60G10;
Secondary 60F20
Posted:
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.
References:
- [1]
- Richard C. Bradley, A stationary, pairwise independent, absolutely regular sequence for which the central limit theorem fails, Probability Theory and Rel. F. 81 (1989), 1-10. MR 90b:60023
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- [4]
- Donald L. Cohn, Measure theory, Birkhäuser, Boston and Stuttgart, 1980. MR 81k:28001
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- [7]
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- [9]
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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:
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
Posted:
July 28, 1999
Communicated by:
James Glimm
Copyright of article:
Copyright
2000,
American Mathematical Society
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