Geodesic
Central limit theorem for hitting times of functionals of Markov jump processes
ESAIM: Probability and Statistics, Tome 8 (2004), pp. 66-75

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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.

DOI : 10.1051/ps:2004002
Classification : 60F05, 60J25, 60K10
Keywords: central limit theorem, hitting time, reliability, failure time 
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     author = {Paroissin, Christian and Ycart, Bernard},
     title = {Central limit theorem for hitting times of functionals of {Markov} jump processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {66--75},
     publisher = {EDP-Sciences},
     volume = {8},
     year = {2004},
     doi = {10.1051/ps:2004002},
     mrnumber = {2085606},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2004002/}
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Paroissin, Christian; Ycart, Bernard. Central limit theorem for hitting times of functionals of Markov jump processes. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 66-75. doi: 10.1051/ps:2004002

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