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Stochastic ordering for continuous-time processes

Part of:Distribution theory - ProbabilityMarkov processes

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 (Y t )t is said to be slower in level crossing than a process (Z t )t if it takes (Y t )t stochastically longer than (Z t )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

Information

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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