In this article, we consider the empirical estimator of the kernel of a semi-Markov process on continuous time with finite state space. We obtain a functional central limit theorem for this estimator in multidimensional form. Next, we present the corresponding theorem for the empirical estimator of the conditional sojourn-time distribution function. The proofs of our results are based on semi-martingales.
- semi-Markov process
- semi-Markov kernel
- empirical estimator
- functional central limit theorem