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A new characterisation property of mixed Poisson processes via Berman's theorem

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Yu Hayakawa
Yu Hayakawa*
Affiliation:
Victoria University of Wellington
*
∗Postal address: School of Mathematical and Computing Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand. Email address: yu.hayakawa@vuw.ac.nz
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Abstract

In the literature on mixed Poisson processes, a number of characterisation properties have been studied. As a new characterisation property for mixed Poisson processes, we show that normalised event occurrence times are the order statistics of independent uniform random variables on (0,1). Berman's theorem on lp-isotropic sequences is applied to prove the results.

Keywords

Berman's theoremexchangeabilityL1-isotropymixed Poisson processes

MSC classification

Primary: 60J99: None of the above, but in this section
Secondary: 60G09: Exchangeability
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 261 - 268
Copyright
Copyright © 2000 by The Applied Probability Trust 

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