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The mean comparison theorem cannot be extended to the Poisson case

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Jan Večeř  and
Mingxin Xu
Jan Večeř*
Affiliation:
Columbia University
Mingxin Xu*
Affiliation:
Carnegie Mellon University
*
∗ Postal address: Department of Statistics, Columbia University, New York, NY 10027, USA. Email address: vecer@stat.columbia.edu
∗∗ Current address: Department of Mathematics and Statistics, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, NC 28223, USA. Email address: mxu2@email.uncc.edu
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Abstract

In this paper, we show that the mean comparison theorem, which is valid for Brownian motion, cannot be extended to Poisson processes. A counterexample in the Poisson case for which the mean comparison theorem does not hold is provided.

Keywords

Comparison theoremPoisson process

MSC classification

Primary: 60G55: Point processes
Secondary: 60J75: Jump processes
Type
Short Communications
Information
Journal of Applied Probability , Volume 41 , Issue 4 , December 2004 , pp. 1199 - 1202
Copyright
Copyright © Applied Probability Trust 2004 

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