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Poisson process via martingale and related characteristics

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Jacek Wesołowski
Jacek Wesołowski*
Affiliation:
Warsaw University of Technology
*
∗Postal address: Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00–661 Warsaw, Poland. Email address: wesolo@alpha.im.pw.edu.pl.
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Abstract

The classical martingale characterizations of the Poisson process were obtained for point process or purely discontinuous martingale i.e. under additional assumptions on properties of trajectories. Here our aim is to search for related characterizations without relying on properties of trajectories. Except for a new martingale characterization, results based on conditional moments jointly involving the past and the nearest future are presented.

Keywords

Poisson processmartingalesconditional variancecharacterizationsconditioning given the futureconditioning given the past

MSC classification

Primary: 60E99: None of the above, but in this section
Type
Short Communications
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 919 - 926
Copyright
Copyright © Applied Probability Trust 1999 

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