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.
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.
@article{AFST_2015_6_24_4_857_0,
author = {Florent Malrieu},
title = {Some simple but challenging {Markov} processes},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {857--883},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 24},
number = {4},
year = {2015},
doi = {10.5802/afst.1468},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1468/}
}
TY - JOUR AU - Florent Malrieu TI - Some simple but challenging Markov processes JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2015 SP - 857 EP - 883 VL - 24 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1468/ DO - 10.5802/afst.1468 LA - en ID - AFST_2015_6_24_4_857_0 ER -
%0 Journal Article %A Florent Malrieu %T Some simple but challenging Markov processes %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2015 %P 857-883 %V 24 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1468/ %R 10.5802/afst.1468 %G en %F AFST_2015_6_24_4_857_0
Florent Malrieu. Some simple but challenging Markov processes. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro Spécial : Conférence “Talking Across Fields” du 24 au 28 mars 2014 à l’Institut de Mathématiques de Toulouse, Tome 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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