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Stochastic ordering for continuous-time processes

Part of: Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

A. Irle
A. Irle*
Affiliation:
Christian-Albrechts-Universität zu Kiel
*
∗ Postal address: Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn Str. 4, D-24098 Kiel, Germany. Email address: irle@math.uni-kiel.de
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Abstract

We consider the following ordering for stochastic processes as introduced by Irle and Gani (2001). A process (Yt)t is said to be slower in level crossing than a process (Zt)t if it takes (Yt)t stochastically longer than (Zt)t to exceed any given level. In Irle and Gani (2001), this ordering was investigated for Markov chains in discrete time. Here these results are carried over to semi-Markov processes with particular attention to birth-and-death processes and also to Wiener processes.

Keywords

Stochastic orderlevel crossingsemi-Markov processesWiener processes

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 2 , June 2003 , pp. 361 - 375
Copyright
Copyright © Applied Probability Trust 2003 

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