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 theorem, hitting time, reliability, failure time

@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://www.numdam.org/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 DA - 2004/// SP - 66 EP - 75 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2004002/ UR - https://www.ams.org/mathscinet-getitem?mr=2085606 UR - https://doi.org/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 https://doi.org/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, Volume 8 (2004), pp. 66-75. doi : 10.1051/ps:2004002. http://www.numdam.org/articles/10.1051/ps:2004002/

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