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
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/3311
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2015-12)
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