Geodesic
Numerical methods for piecewise deterministic Markov processes with boundary
Ludovic Goudenège1
1 Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS - UMR 8050) Université Paris-Est, 5 boulevard Descartes Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France
ESAIM. Proceedings, Tome 45 (2014), pp. 338-348.

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In this paper is described the general aspect of a numerical method for piecewise deterministic Markov processes with boundary. Under very natural hypotheses, a crucial result about uniqueness of solution of a generalized Kolmogorov equation with respect to a test function space is proved. Next we prove the existence and uniqueness of a positive solution to the finite volume scheme without result about convergence. Finally different models of transmission control protocol window-size processes are simulated to illustrate the efficiency of the numerical method for describing the evolution of the density of a piecewise deterministic Markov process with boundary. Obviously some technical aspects have been skipped for reader convenience but the full theory will be exposed in a forthcoming paper in collaboration with C. Cocozza-Thivent, R. Eymard and M. Roussignol.
DOI : 10.1051/proc/201445035

Ludovic Goudenège 1

1 Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS - UMR 8050) Université Paris-Est, 5 boulevard Descartes Champs sur Marne, 77454 Marne-la-Vallée Cedex 2, France 
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     title = {Numerical methods for piecewise deterministic {Markov} processes with boundary},
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Ludovic Goudenège. Numerical methods for piecewise deterministic Markov processes with boundary. ESAIM. Proceedings, Tome 45 (2014), pp. 338-348. doi : 10.1051/proc/201445035. http://geodesic.mathdoc.fr/articles/10.1051/proc/201445035/

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