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On the Weak Convergence of an Empirical Estimator of the Discrete-Time Semi-Markov Kernel

In: Applications of Mathematics and Informatics in Military Science

Author

Listed:
  • Stylianos Georgiadis

    (Université de Technologie de Compiègne Centre de Recherches de Royallieu)

  • Nikolaos Limnios

    (Université de Technologie de Compiègne Centre de Recherches de Royallieu)

Abstract

In this chapter, we consider the discrete-time semi-Markov processes with finite state space and the empirical estimator of the semi-Markov kernel. The basic definitions concerning the semi-Markov processes are presented. We study the weak convergence of the empirical estimator of the discrete-time semi-Markov kernel. Next, we present the corresponding weak convergence theorem for the empirical estimator of some related measures. The proofs of our results are based on semimartingales.

Suggested Citation

  • Stylianos Georgiadis & Nikolaos Limnios, 2012. "On the Weak Convergence of an Empirical Estimator of the Discrete-Time Semi-Markov Kernel," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Military Science, edition 127, chapter 0, pages 221-239, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-4109-0_14
    DOI: 10.1007/978-1-4614-4109-0_14
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