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Some characterizations of partial exchangeability

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

B. G. Ivanoff  and
N. C. Weber
B. G. Ivanoff
Affiliation:
Department of Mathematics University of OttawaOttawa, Ontario Canada K1N 6N5
N. C. Weber
Affiliation:
School of Mathematics and Statistics University of Sydney NSW 2006, Australia
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Abstract

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Kallenberg [2] introduced the concept of F-exchangeable sequences of random variables and produced some characterizations of F-exchangeability in terms of stopping times. In this paper ways of extending the concept of F-exchangeability to doubly indexed arrays of random variables are explored and some characterizations obtained for row and column exchangebale arrays, weakly exchangeable arrays and separately exchangeable continuous processes.

Keywords

Row and column exchangeable arraysstopping timesweakly exchangeable arraysmartingalesseparately exchangeable processes

MSC classification

Secondary: 60G09: Exchangeability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 345 - 359
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Dacunha-Castelle, D., ‘Indiscemability and exchangeability in L p spaces’, in: Proc. Seminar on Random Series, Convex Sets and Geometry of Banach Spaces (Aarhus, 1974) pp. 50–56.Google Scholar
[2]Kallenberg, O., ‘Characterizations and embedding properties in exchangeability’, Z. Wahrsch. Verw. Gebiete 60 (1982), 249–281.CrossRefGoogle Scholar
[3]Kingman, J. F. C., ‘Uses of exchangeability’, Ann. Probab. 6 (1978), 183–197.CrossRefGoogle Scholar