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Shot noise Cox processes

Part of: Special processes Geometric probability and stochastic geometry Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Jesper Møller
Jesper Møller*
Affiliation:
Aalborg University
*
∗ Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. Email address: [email protected]
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Abstract

Shot noise Cox processes constitute a large class of Cox and Poisson cluster processes in ℝd, including Neyman-Scott, Poisson-gamma and shot noise G Cox processes. It is demonstrated that, due to the structure of such models, a number of useful and general results can easily be established. The focus is on the probabilistic aspects with a view to statistical applications, particularly results for summary statistics, reduced Palm distributions, simulation with or without edge effects, conditional simulation of the intensity function and local and spatial Markov properties.

Keywords

Conditional simulationCox processedge effectMarkov point processnearest-neighbour Markov point processNeyman-Scott processPalm distributionPoisson cluster processPoisson-gamma processshot noise G Cox processsimulationspatial point processsummary statistics

MSC classification

Primary: 60D05: Geometric probability and stochastic geometry 60G55: Point processes 62M30: Spatial processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 68U20: Simulation
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 614 - 640
Copyright
Copyright © Applied Probability Trust 2003 

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