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Characterisation of a multivariate stochastic ordering

Published online by Cambridge University Press:  17 April 2009

Colm Art O'Cinneide
Colm Art O'Cinneide
Affiliation:
Statistics Division, Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, United States of America
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Abstract

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The multivariate stochastic ordering induced by the convex nondecreasing functions compares a combination of size and variability of random vectors. Closely following methods developed by Strassen, we show that two probability measures are ordered in this way if and only if they are the marginals of some submartingale. The implications of this in majorisation theory are discussed.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 387 - 392
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Marshall, A.W. and Olkin, I., Inequalities: Theory of Majorization and its Applications (Academic Press, New York, 1979).Google Scholar
[2]Rockafellar, R.T., Conves Analysis (Princeton University Press, Princeton, New Jersey, 1970).Google Scholar
[3]Stoyan, D., Comparison Mathods for Queues and other Stochastic Models (John Wiley, New York, 1983).Google Scholar
[4]Strassen, V., ‘The existence of probability measures with given marginals’, Ann. Math. Statist. 36 (1965), 423–439.Google Scholar
[5]Whitt, W., ‘The effect of variability in the GI/G/s Queue’, J. Appl. Probab. 17 (1980), 1062–1071.Google Scholar