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The permanental process

Published online by Cambridge University Press:  08 September 2016

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: [email protected]
∗∗ 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

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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.

MSC classification

Type
Stochastic Geometry and Statistical Applications
Copyright
Copyright © Applied Probability Trust 2006 

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