Displaying similar documents to “Asymptotic normality of the kernel estimate for the Markovian transition operator”

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.

Estimation of the transition density of a Markov chain

Mathieu Sart (2014)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We present two data-driven procedures to estimate the transition density of an homogeneous Markov chain. The first yields a piecewise constant estimator on a suitable random partition. By using an Hellinger-type loss, we establish non-asymptotic risk bounds for our estimator when the square root of the transition density belongs to possibly inhomogeneous Besov spaces with possibly small regularity index. Some simulations are also provided. The second procedure is of theoretical interest...

On the exchanges between Wolfgang Doeblin and Bohuslav Hostinský

Laurent Mazliak (2007)

Revue d'histoire des mathématiques

Similarity:

We present the letters sent by Wolfgang Doeblin to Bohuslav Hostinský between 1936 and 1938. They concern some aspects of the general theory of Markov chains and the solutions of the Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis.