Open Access
August 2019 Mixing properties and central limit theorem for associated point processes
Arnaud Poinas, Bernard Delyon, Frédéric Lavancier
Bernoulli 25(3): 1724-1754 (August 2019). DOI: 10.3150/18-BEJ1033


Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated. We prove $\alpha $-mixing properties for associated spatial point processes by controlling their $\alpha $-coefficients in terms of the first two intensity functions. A central limit theorem for functionals of associated point processes is deduced, using both the association and the $\alpha $-mixing properties. We discuss in detail the case of DPPs, for which we obtain the limiting distribution of sums, over subsets of close enough points of the process, of any bounded function of the DPP. As an application, we get the asymptotic properties of the parametric two-step estimator of some inhomogeneous DPPs.


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Arnaud Poinas. Bernard Delyon. Frédéric Lavancier. "Mixing properties and central limit theorem for associated point processes." Bernoulli 25 (3) 1724 - 1754, August 2019.


Received: 1 May 2017; Revised: 1 February 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066237
MathSciNet: MR3961228
Digital Object Identifier: 10.3150/18-BEJ1033

Keywords: determinantal point process , negative association , Parametric estimation , positive association , Strong mixing

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

Vol.25 • No. 3 • August 2019
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