Exchangeable Occupancy Models and Discrete Processes with the Generalized Uniform Order Statistics Property

Details Exchangeable Occupancy Models and Discrete Processes with the Generalized Uniform Order Statistics Property Exchangeable Occupancy Models and Discrete Processes with the Generalized Uniform Order Statistics Property

2011-12-05

arxiv.org/abs/1112.0867v1

Mathematics

Probability

23 pages

Scientific paper

This work focuses on Exchangeable Occupancy Models (EOM) and their relations with the Uniform Order Statistics Property (UOSP) for point processes in discrete time. As our main purpose, we show how definitions and results presented in Shaked, Spizzichino and Suter (2004) can be unified and generalized in the frame of occupancy models. We first show some general facts about EOM's. Then we introduce a class of EOM's, called $\mathcal{M}^{(a)}$-models, that is used for generalizing the notion of Uniform Order Statistics Property. For processes with this property, we prove a general characterization result. Our interest is also focused on properties of closure w.r.t. some natural transformations of EOM's.

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