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

Romain Azaïs

ESAIM: Probability and Statistics (2014)

  • Volume: 18, page 726-749
  • ISSN: 1292-8100

Abstract

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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 invariant measures. We state a result of consistency and a central limit theorem under some general assumptions about the main features of the process. A simulation study illustrates the well asymptotic behavior of our estimator.

How to cite

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Azaïs, Romain. "A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process." ESAIM: Probability and Statistics 18 (2014): 726-749. <http://eudml.org/doc/274391>.

@article{Azaïs2014,
abstract = {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 invariant measures. We state a result of consistency and a central limit theorem under some general assumptions about the main features of the process. A simulation study illustrates the well asymptotic behavior of our estimator.},
author = {Azaïs, Romain},
journal = {ESAIM: Probability and Statistics},
keywords = {piecewise-deterministic Markov processes; nonparametric estimation; recursive estimator; transition kernel; asymptotic consistency},
language = {eng},
pages = {726-749},
publisher = {EDP-Sciences},
title = {A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process},
url = {http://eudml.org/doc/274391},
volume = {18},
year = {2014},
}

TY - JOUR
AU - Azaïs, Romain
TI - A recursive nonparametric estimator for the transition kernel of a piecewise-deterministic Markov process
JO - ESAIM: Probability and Statistics
PY - 2014
PB - EDP-Sciences
VL - 18
SP - 726
EP - 749
AB - 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 invariant measures. We state a result of consistency and a central limit theorem under some general assumptions about the main features of the process. A simulation study illustrates the well asymptotic behavior of our estimator.
LA - eng
KW - piecewise-deterministic Markov processes; nonparametric estimation; recursive estimator; transition kernel; asymptotic consistency
UR - http://eudml.org/doc/274391
ER -

References

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