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Central limit theorem for hitting times of functionals of Markov jump processes

Published online by Cambridge University Press:  15 September 2004

Christian Paroissin  and
Bernard Ycart
Christian Paroissin
Affiliation:
Laboratoire MAP5, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France; parc@math-info.univ-paris5.fr., ycart@math-info.univ-paris5.fr.
Bernard Ycart
Affiliation:
Laboratoire MAP5, 45 rue des Saints-Pères, 75270 Paris Cedex 06, France; parc@math-info.univ-paris5.fr., ycart@math-info.univ-paris5.fr.
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Abstract

A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.

Keywords

Central limit theoremhitting timereliabilityfailure time.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 66 - 75
Copyright
© EDP Sciences, SMAI, 2004

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