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The permanental process

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  08 September 2016

Peter McCullagh  and
Jesper Møller
Peter McCullagh*
Affiliation:
University of Chicago
Jesper Møller*
Affiliation:
Aalborg University
*
∗ Postal address: Department of Statistics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA. Email address: pmcc@galton.uchicago.edu
∗∗ Postal address: Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, DK-9220 Aalborg, Denmark. Email address: jm@math.auc.dk
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Abstract

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We extend the boson process first to a large class of Cox processes and second to an even larger class of infinitely divisible point processes. Density and moment results are studied in detail. These results are obtained in closed form as weighted permanents, so the extension is called a permanental process. Temporal extensions and a particularly tractable case of the permanental process are also studied. Extensions of the fermion process along similar lines, leading to so-called determinantal processes, are discussed.

Keywords

Boson processCox processdensity of spatial point processdeterminantal processfactorial moment measurefermion processGaussian processinfinite divisibilitysimulationspatio-temporal processweighted permanent

MSC classification

Primary: 60G55: Point processes
Secondary: 62M30: Spatial processes
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 38 , Issue 4 , December 2006 , pp. 873 - 888
Copyright
Copyright © Applied Probability Trust 2006 

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