On the Strong Brillinger-Mixing Property of Alpha-Determinantal Point Processes and Some Applications
- First we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function C(x,y) defining an alpha-determinantal point process (DPP). Assuming absolute integrability of the function C_0(x) = C(o,x) we show that a stationary alpha-DPP with kernel function C_0(x) is "strongly" Brillinger-mixing implying, among others, that its tail-sigma-field is trivial. Second we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications to statistical second-order analysis of alpha-DPPs.
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| Author: | Lothar HeinrichGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-33113 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/3311 |
| Series (Serial Number): | Preprints des Instituts für Mathematik der Universität Augsburg (2015-12) |
| Type: | Preprint |
| Language: | English |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2015/09/24 |
| Tag: | determinantal and permanental point process; trivial tail-sigma-field; exponential moment; shot-noise process; Berry-Esseen bound; multiparameter K-function; kernel-type product density estimator; goodness-of-fit test |
| GND-Keyword: | Punktprozess; Anpassungstest; Schrotrauschen; Dichteschätzung; Berry-Esseen-Abschätzung |
| 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 |
