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