Uniform Order Statistics Property and ℓ∞-Spherical Densities

  • Authors:

  • Moshe Shaked;Fabio Spizzichino;Florentina Suter

  • Affiliations:

  • Department of Mathematics, University of Arizona, Tucson, AZ 85721, E-mail: shaked@math.arizona.edu;Department of Mathematics, University “La Sapienza”, Piazzale Aldo Moro, 5, 00185 Rome, Italy;Department of Mathematics, University of Bucharest, Academiei 14, 010014 Bucharest, Romania

  • Venue:
  • Probability in the Engineering and Informational Sciences
  • Year:
  • 2004

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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 ℓ∞≤-spherical density, n ≥ 1. Some related results, and some further properties of ℓ∞≤-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.