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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.
@article{PS_2004__8__66_0,
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/}
}
TY - JOUR AU - Paroissin, Christian AU - Ycart, Bernard TI - Central limit theorem for hitting times of functionals of Markov jump processes JO - ESAIM: Probability and Statistics PY - 2004 SP - 66 EP - 75 VL - 8 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ps:2004002/ DO - 10.1051/ps:2004002 LA - en ID - PS_2004__8__66_0 ER -
%0 Journal Article %A Paroissin, Christian %A Ycart, Bernard %T Central limit theorem for hitting times of functionals of Markov jump processes %J ESAIM: Probability and Statistics %D 2004 %P 66-75 %V 8 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ps:2004002/ %R 10.1051/ps:2004002 %G en %F PS_2004__8__66_0
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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