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A martingale characterization of Pólya-Lundberg processes

Part of: Stochastic processes Distribution theory

Published online by Cambridge University Press:  14 July 2016

Birgit Niese
Birgit Niese*
Affiliation:
Darmstadt University of Technology
*
∗Postal address: Department of Mathematics, Darmstadt University of Technology, Schloßgartenstraße 7, D-64289 Darmstadt, Germany. Email address: niese@mathematik.tu-darmstadt.de
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Abstract

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We study exponential families within the class of counting processes and show that a mixed Poisson process belongs to an exponential family if and only if it is either a Poisson process or has a gamma structure distribution. This property can be expressed via exponential martingales.

Keywords

Mixed Poisson processPólya-Lundberg processexponential family

MSC classification

Primary: 60G55: Point processes
Secondary: 62E99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 43 , Issue 3 , September 2006 , pp. 741 - 754
Copyright
© Applied Probability Trust 2006 

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