Absolute Regularity and Brillinger Mixing of Stationary Point Processes

  • We study the following problem: How to verify Brillinger-mixing of stationary point processes in Rd by imposing conditions on a suitable mixing coefficient? For this, we define an absolute regularity (or beta-mixing) coefficient for point processes and derive an explicit condition in terms of this coefficient which implies finite total variation of the kth-order reduced factorial cumulant measure of the point process for fixed k >= 2. To prove this, we introduce higher-order covariance measures and use Statulevicius' representation formula for mixed cumulants in case of random (counting) measures. To illustrate our results, we consider some Brillinger-mixing point processes occurring in stochastic geometry.

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Author:Lothar HeinrichGND, Zbynek Pawlas
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2207
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-02)
Publishing Institution:Universität Augsburg
Release Date:2013/01/24
stationary point process; stochastic geometry; mixing properties
GND-Keyword:Stationärer Punktprozess; Stochastische Geometrie; Mischung <Mathematik>
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Stochastik und ihre Anwendungen
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand