Piecewise deterministic Markov process — recent results

Abstract

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