Volume 45, September 2014Congrès SMAI 2013
|Page(s)||338 - 348|
|Published online||13 November 2014|
Numerical methods for piecewise deterministic Markov processes with boundary
Laboratoire d’Analyse et de
Mathématiques Appliquées (CNRS - UMR 8050) Université Paris-Est,
5 boulevard Descartes Champs sur
Marne-la-Vallée Cedex 2,
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.
© EDP Sciences, SMAI 2014
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