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Spreadable arrays and martingale structures

Part of: Stochastic processes

Published online by Cambridge University Press:  09 April 2009

B. Gail Ivanoff  and
N. C. Weber
B. Gail Ivanoff
Affiliation:
Department of Mathematics and Statistics, University of Ottawa, PO Box 450 Station A, Ottawa, Ontario, Canada, K1N 6N5, e-mail: givanoff@uottawa.ca
N. C. Weber
Affiliation:
School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia, e-mail: neville@maths.usyd.edu.au
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Abstract

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Kallenberg has introduced the concept of conditional spreadability for random sequences and has developed characterizations of this property in terms of one dimensional martingales and optional times, and as well has proven a predictable sampling theorem. This paper investigates the relationship between planar martingale structures and the natural analogues of conditional spreadability when extended to arrays of random elements. Analogues of the predictable sampling theorem are also established for spreadable arrays.

Keywords

spreadable arraycontractable arrayexchangeable arraymartingaleadapted timepredictable sampling.

MSC classification

Secondary: 60G09: Exchangeability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 277 - 296
Copyright
Copyright © Australian Mathematical Society 2005

References

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