| Issue |
ESAIM: PS
Volume 8, August 2004
|
|
|---|---|---|
| Page(s) | 66 - 75 | |
| DOI | https://doi.org/10.1051/ps:2004002 | |
| Published online | 15 September 2004 | |
Central limit theorem for hitting times of functionals of Markov jump processes
Laboratoire MAP5,
45 rue des Saints-Pères, 75270 Paris Cedex 06, France; parc@math-info.univ-paris5.fr.,
ycart@math-info.univ-paris5.fr.
Received:
18
July
2003
Revised:
24
May
2003
Revised:
13
October
2003
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.
Mathematics Subject Classification: 60F05 / 60J25 / 60K10
Key words: Central limit theorem / hitting time / reliability / failure time.
© EDP Sciences, SMAI, 2004
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