Displaying similar documents to “From equivalent linear equations to Gauss-Markov theorem.”

A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process

Romain Azaïs (2014)

ESAIM: Probability and Statistics

Similarity:

In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a piecewise-deterministic Markov process, from only one observation of the path within a long time. In this framework, we do not observe a Markov chain with transition kernel of interest. Fortunately, one may write the transition density of interest as the ratio of the invariant distributions of two embedded chains of the process. Our method consists in estimating these...

The expected cumulative operational time for finite semi-Markov systems and estimation

Brahim Ouhbi, Ali Boudi, Mohamed Tkiouat (2007)

RAIRO - Operations Research

Similarity:

In this paper we, firstly, present a recursive formula of the empirical estimator of the semi-Markov kernel. Then a non-parametric estimator of the expected cumulative operational time for semi-Markov systems is proposed. The asymptotic properties of this estimator, as the uniform strongly consistency and normality are given. As an illustration example, we give a numerical application.