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

ESAIM: Probability and Statistics (2014)

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

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topAzaïs, 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 -

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