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On negative association of some finite point processes on general state spaces

Part of: Markov processes Special processes

Published online by Cambridge University Press:  12 July 2019

Günter Last  and
Ryszard Szekli
Günter Last*
Affiliation:
Karlsruhe Institute of Technology
Ryszard Szekli*
Affiliation:
University of Wroclaw
*
*Postal address: Department of Mathematics, Karlsruhe Institute of Technology, Englerstr. 2, D-76131, Karlsruhe, Germany.
**Postal address: University of Wrocław, Mathematical Institute, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland. Email address: ryszard.szekli@uwr.edu.pl
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Abstract

We study negative association for mixed sampled point processes and show that negative association holds for such processes if a random number of their points fulfils the ultra log-concave (ULC) property. We connect the negative association property of point processes with directionally convex dependence ordering, and show some consequences of this property for mixed sampled and determinantal point processes. Some applications illustrate the general theory.

Keywords

Finite point processmixed sampled point processnegative associationstrong Rayleigh measureULC

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 1 , March 2019 , pp. 139 - 152
Copyright
© Applied Probability Trust 2019 

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