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Compensator conditions for stochastic ordering of point processes

Published online by Cambridge University Press:  14 July 2016

A. Kwieciński  and
R. Szekli
A. Kwieciński
Affiliation:
University of Wroctaw
R. Szekli*
Affiliation:
University of Wroctaw
*
∗ Postal address for both authors: Mathematical Institute, University of Wroclaw, pl. Grunwaldzki 2/4, 50–384 Wroclaw, Poland.
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Abstract

Sufficient conditions are given under which two simple point processes on the positive half-line can be stochastically compared as random elements of D(0,∞) or R∞+ Using a martingale approach to point processes, the conditions are proposed via a compensator function family. Appropriate versions of the processes being compared are constructed on the same probability space. The results are illustrated by replacement policies and semi-Markov point processes.

Keywords

COMPENSATORREPLACEMENT POLICYSEMI-MARKOV POINT PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 4 , December 1991 , pp. 751 - 761
Copyright
Copyright © Applied Probability Trust 1991 

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