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Some simple but challenging Markov processes
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 857-883.

In this note, we present few examples of Piecewise Deterministic Markov Processes and their long time behavior. They share two important features: they are related to concrete models (in biology, networks, chemistry,...) and they are mathematically rich. Their mathematical study relies on coupling method, spectral decomposition, PDE technics, functional inequalities. We also relate these simple examples to recent and open problems.

Ces notes rassemblent l’étude du comportement en temps long de plusieurs processus de Markov déterministes par morceaux. Ces processus ont le double intérêt d’être motivés par la modélisation (biologie, réseaux de communication, chimie,...) et d’impliquer de nombreux outils mathématiques : couplage, approches spectrales, équations aux dérivées partielles non locales ou encore inégalités fonctionnelles. Ces exemples permettent enfin de formuler des questions ouvertes.

Published online:
DOI: 10.5802/afst.1468
Florent Malrieu 1

1 Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 6083), Fédération Denis Poisson (FR CNRS 2964), Université François-Rabelais, Parc de Grandmont, 37200 Tours, France.
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Florent Malrieu. Some simple but challenging Markov processes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 24 (2015) no. 4, pp. 857-883. doi : 10.5802/afst.1468. https://afst.centre-mersenne.org/articles/10.5802/afst.1468/

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