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

Stylianos Georgiadis, Nikolaos Limnios

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearch

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.
Original languageEnglish
Title of host publicationApplications of Mathematics and Informatics in Military Science
PublisherSpringer
Publication date2012
Pages221-239
Chapter14
ISBN (Print)978-1-4614-4108-3
ISBN (Electronic)978-1-4614-4109-0
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Discrete-time semi-Markov kernel
  • Empirical estimator
  • Weak convergence
  • Invariance principle
  • Semimartingales

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