KERNEL SMOOTHING OF THE MEAN PERFORMANCE FOR HOMOGENEOUS CONTINUOUS TIME SEMI-MARKOV PROCESS

The main goal of the present paper is to propose a systematic approach to model performance measurements within the context of continuous-time semi-Markov processes with a finite state space. Specifically, the mean performance is estimated using the kernel method. The uniform strong consistency and the asymptotic normality of the proposed estimator is investigated. Furthermore, a non-parametric kernel estimation of the expected cumulative operational time is addressed. The constructed estimator is proved to be consistent and to converge to a normal random variable as the time of observation becomes large. As an illustration example, a simulation study has been conducted in order to highlight the efficiency as well as the superiority of our method to the standard empirical method.