LEVY-BASED COX POINT PROCESSES

In this paper we introduce Levy-driven Cox point processes (LCPs) as Cox point processes with driving intensity function A defined by a kernel smoothing of a Levy basis (an independently scattered, infinitely divisible random measure). We also consider log Levy-driven Cox point processes (LLCPs) with A 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 Levy-based Cox processes, including moment properties described by nth-order product densities, mixing properties, specification of inhomogeneity, and spatio-temporal extensions.