A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process
AZAÏS, Romain
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
AZAÏS, Romain
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
< Reduce
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]
Language
en
Article de revue
This item was published in
ESAIM: Probability and Statistics. 2014, vol. 18, p. 726-749
EDP Sciences
English Abstract
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary piecewise-deterministic Markov process, from only one observation of the path within a ...Read more >
In this paper, we investigate a nonparametric approach to provide a recursive estimator of the transition density of a non-stationary 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 invariant measures. We state a result of consistency under some general assumptions about the main features of the process. A simulation study illustrates the well asymptotic behavior of our estimator.Read less <
Origin
Hal imported