AZAÏS, Romain; BARDET, Jean-Baptiste; GENADOT, Alexandre; KRELL, Nathalie; ZITT, Pierre-André

doi:10.1051/proc/201444017

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AZAÏS, Romain
Institut de Mathématiques de Bordeaux [IMB]

BARDET, Jean-Baptiste
Laboratoire de Mathématiques Raphaël Salem [LMRS]

GENADOT, Alexandre
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]

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Article de revue

Ce document a été publié dans

ESAIM: Proceedings. 2014, vol. 44, p. 276-290

EDP Sciences

Résumé en anglais

We give a short overview of recent results on a specific class of Markov process: the Piecewise Deterministic Markov Processes (PDMPs). We first recall the definition of these processes and give some general results. On more specific cases such as the TCP model or a model of switched vector fields, better results can be proved, especially as regards long time behaviour. We continue our review with an infinite dimensional example of neuronal activity. From the statistical point of view, these models provide specific challenges: we illustrate this point with the example of the estimation of the distribution of the inter-jumping times. We conclude with a short overview on numerical methods used for simulating PDMPs.< Réduire

Mots clés en anglais

Ergodicity

Piecewise-deterministic Markov process

Jump processes

ergodicity of Markov chains

nonparametric estimation

Switched dynamical systems

Wasserstein distance

Coupling

numerical method

Ergodicity.

URI

https://oskar-bordeaux.fr/handle/20.500.12278/189574

DOI

http://dx.doi.org/10.1051/proc/201444017

Project ANR

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251