Abstract
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.
| Original language | English |
|---|---|
| Journal | Journal of Nonparametric Statistics |
| Volume | 24 |
| Issue number | 4 |
| Pages (from-to) | 1007-1017 |
| ISSN | 1048-5252 |
| DOIs | |
| Publication status | Published - 2012 |
| Externally published | Yes |
Keywords
- semi-Markov process
- semi-Markov kernel
- empirical estimator
- functional central limit theorem
- semi-martingales
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