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UNIFORM ORDER STATISTICS PROPERTY AND [ell ]-SPHERICAL DENSITIES

Published online by Cambridge University Press:  01 July 2004

Moshe Shaked
Affiliation:
Department of Mathematics, University of Arizona, Tucson, AZ 85721, E-mail: shaked@math.arizona.edu
Fabio Spizzichino
Affiliation:
Department of Mathematics, University “La Sapienza”, Piazzale Aldo Moro, 5, 00185 Rome, Italy
Florentina Suter
Affiliation:
Department of Mathematics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania

Abstract

In this article, we observe that processes with the uniform order statistics property (UOSP) can be characterized by the condition that their first n epoch times have a joint [ell ]-spherical density, n ≥ 1. Some related results, and some further properties of [ell ]-spherical densities, are also given. We also extend some of the results regarding the UOSP to the more general (not necessarily uniform) order statistics property. Finally, we develop a theory of discrete-time discrete-state processes with the UOSP, where the need to consider multiple jumps, at a single time point, arises.

Type
Research Article
Copyright
© 2004 Cambridge University Press

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References

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