Advances in Applied Probability

Lévy-based Cox point processes

Gunnar Hellmund, Michaela Prokešová, and Eva B. Vedel Jensen

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In this paper we introduce Lévy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function Λ defined by a kernel smoothing of a Lévy basis (an independently scattered, infinitely divisible random measure). We also consider log Lévy-driven Cox point processes (LLCPs) with Λ equal to the exponential of such a kernel smoothing. Special cases are shot noise Cox processes, log Gaussian Cox processes, and log shot noise Cox processes. We study the theoretical properties of Lévy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.

Article information

Adv. in Appl. Probab. Volume 40, Number 3 (2008), 603-629.

First available in Project Euclid: 1 October 2008

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Mathematical Reviews number (MathSciNet)

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 60G55: Point processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Cox process infinitely divisible distribution inhomogeneity kernel smoothing Lévy basis log Gaussian Cox process mixing product density shot noise Cox process


Hellmund, Gunnar; Prokešová, Michaela; Vedel Jensen, Eva B. Lévy-based Cox point processes. Adv. in Appl. Probab. 40 (2008), no. 3, 603--629. doi:10.1239/aap/1222868178.

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