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 |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-22072 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/2207 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2013-02) |
| Type: | Preprint |
| Language: | English |
| Date of Publication (online): | 2013/01/24 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2013/01/24 |
| Tag: | Mischungseigenschaften mixing properties; stationary point process; stochastic geometry |
| 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 |
