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Brillinger mixing of determinantal point processes and statistical applications. (English) Zbl 1403.60039
Summary: Stationary determinantal point processes are proved to be Brillinger mixing. This property is an important step towards asymptotic statistics for these processes. As an important example, a central limit theorem for a wide class of functionals of determinantal point processes is established. This result yields in particular the asymptotic normality of the estimator of the intensity of a stationary determinantal point process and of the kernel estimator of its pair correlation.

MSC:
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F05 Central limit and other weak theorems
62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference
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