Geodesic
Probabilistic and Piecewise Deterministic models in Biology
Bertrand Cloez1 ; Renaud Dessalles2 ; Alexandre Genadot3 ; Florent Malrieu4 ; Aline Marguet5 ; Romain Yvinec6
1 MISTEA, INRA, Montpellier SupAgro, Univ. Montpellier, France.
2 INRA, UR MaIAGE, domaine de Vilvert, Jouy en Josas, France.
3 Institut de Mathématiques de Bordeaux, Inria Bordeaux-Sud-Ouest, France.
4 Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François-Rabelais, Parc de Grandmont, 37200 Tours, France.
5 CMAP, École Polytechnique, Université Paris-Saclay, Palaiseau, France.
6 Physiologie de la Reproduction et des Comportements, Institut National de la Recherche Agronomique (INRA) UMR85, CNRS-Université François-Rabelais UMR7247, IFCE, Nouzilly, 37380 France
ESAIM. Proceedings, Tome 60 (2017), pp. 225-245.

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We present recent results on Piecewise Deterministic Markov Processes (PDMPs), involved in biological modeling. PDMPs, first introduced in the probabilistic literature by [30], are a very general class of Markov processes and are being increasingly popular in biological applications. They also give new interesting challenges from the theoretical point of view. We give here different examples on the long time behavior of switching Markov models applied to population dynamics, on uniform sampling in general branching models applied to structured population dynamic, on time scale separation in integrate-and-fire models used in neuroscience, and, finally, on moment calculus in stochastic models of gene expression.
DOI : 10.1051/proc/201760225

Bertrand Cloez 1 ; Renaud Dessalles 2 ; Alexandre Genadot 3 ; Florent Malrieu 4 ; Aline Marguet 5 ; Romain Yvinec 6

1 MISTEA, INRA, Montpellier SupAgro, Univ. Montpellier, France.
2 INRA, UR MaIAGE, domaine de Vilvert, Jouy en Josas, France.
3 Institut de Mathématiques de Bordeaux, Inria Bordeaux-Sud-Ouest, France.
4 Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François-Rabelais, Parc de Grandmont, 37200 Tours, France.
5 CMAP, École Polytechnique, Université Paris-Saclay, Palaiseau, France.
6 Physiologie de la Reproduction et des Comportements, Institut National de la Recherche Agronomique (INRA) UMR85, CNRS-Université François-Rabelais UMR7247, IFCE, Nouzilly, 37380 France 
@article{EP_2017_60_a12,
     author = {Bertrand Cloez and Renaud Dessalles and Alexandre Genadot and Florent Malrieu and Aline Marguet and Romain Yvinec},
     title = {Probabilistic and {Piecewise} {Deterministic} models in {Biology}},
     journal = {ESAIM. Proceedings},
     pages = {225--245},
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     doi = {10.1051/proc/201760225},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201760225/}
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Bertrand Cloez; Renaud Dessalles; Alexandre Genadot; Florent Malrieu; Aline Marguet; Romain Yvinec. Probabilistic and Piecewise Deterministic models in Biology. ESAIM. Proceedings, Tome 60 (2017), pp. 225-245. doi : 10.1051/proc/201760225. http://geodesic.mathdoc.fr/articles/10.1051/proc/201760225/

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