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Ageing first-passage times of Markov processes: a matrix approach

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Haijun Li  and
Moshe Shaked
Haijun Li*
Affiliation:
Washington State University
Moshe Shaked*
Affiliation:
University of Arizona
*
∗Postal address: Department of Pure and Applied Mathematics, Washington State University, Pullman, Washington 99164, USA. email:[email protected]
∗∗Postal address: Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA. email:[email protected]
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Abstract

Using a matrix approach we discuss the first-passage time of a Markov process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first-passage time possesses various ageing properties are studied. Some results previously obtained by Li and Shaked (1995) are extended.

Keywords

STOCHASTIC MONOTONICITYMONOTONE TRANSITION MATRIXCONVEX TRANSITION MATRIXFIRST-PASSAGE TIMESLIFE DISTRIBUTIONSRELIABILITY THEORY

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 1 - 13
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Supported by NSF Grant DMS 9303891.

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