Central limit theorem for hitting times of functionals of Markov jump processes
Résumé
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 proof uses a functional central limit theorem for the sum, together with exponential bounds on the tail probabilities. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.