Untitled
Language
en
Article de revue
This item was published in
ESAIM: Proceedings. 2014, vol. 44, p. 276-290
EDP Sciences
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Ergodicity
Piecewise-deterministic Markov process
Jump processes
ergodicity of Markov chains
nonparametric estimation
Switched dynamical systems
Wasserstein distance
Coupling
numerical method
Ergodicity.
ANR Project
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Origin
Hal imported