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A multidimensional functional central limit theorem for an empirical estimator of a continuous-time semi-Markov kernel

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  • S. Georgiadis
  • N. Limnios

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.

Suggested Citation

  • S. Georgiadis & N. Limnios, 2012. "A multidimensional functional central limit theorem for an empirical estimator of a continuous-time semi-Markov kernel," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1007-1017, December.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:4:p:1007-1017
    DOI: 10.1080/10485252.2012.715162
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    Cited by:

    1. Salim Bouzebda & Chrysanthi Papamichail & Nikolaos Limnios, 2018. "On a multidimensional general bootstrap for empirical estimator of continuous-time semi-Markov kernels with applications," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 49-86, January.

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