Scaling limits of stationary determinantal shot-noise fields

2023/03/09 by Takumi Aburayama, Aburayama, Takumi, Naoto Miyoshi +1
Economics, Econometrics and Finance · #60F05 (Secondary) #60G55 (Primary) 60G60 #FOS: Mathematics #G.3 #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2303.05011

openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a shot-noise field defined on a stationary determinantal point process on ℝ^d associated with i.i.d. amplitudes and a bounded response function, for which we investigate the scaling limits as the intensity of the point process goes to infinity. Specifically, we show that the centralized and suitably scaled shot-noise field converges in finite dimensional distributions to i) a Gaussian random field when the amplitudes have the finite second moment and ii) an α-stable random field when the amplitudes follow a regularly varying distribution with index -α for α∈(1,2). We first prove the corresponding results for the shot-noise field defined on a homogeneous Poisson point process and then extend them to the one defined on a stationary determinantal point process.

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