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Preservation of Stochastic Orderings under Random Mapping by Point Processes

Published online by Cambridge University Press:  27 July 2009

Moshe Shaked  and
Tityik Wong
Moshe Shaked
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721
Tityik Wong
Affiliation:
Applied Mathematics Program, University of Arizona, Tucson, Arizona 85721
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Abstract

Let N = [N(t), t ≥ 0] be a point process, and let T1 and T2 be two positive random variables that are independent of N. Define Mk = N(Tk), k = 1,2. In this paper we study conditions on the process N under which some stochastic orders between T1 and T2 are transformed into stochastic orders between M1 and M2. In some cases the converses are also shown to be true. Some applications and examples are given.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 4 , October 1995 , pp. 563 - 580
Copyright
Copyright © Cambridge University Press 1995

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