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Article Dans Une Revue ESAIM: Proceedings and Surveys Année : 2014

Numerical methods for piecewise deterministic Markov processes with boundary

Résumé

In this paper is described the general aspect of a numerical method for piecewise determin-istic 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.
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hal-01902024 , version 1 (23-10-2018)

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Ludovic Goudenège. Numerical methods for piecewise deterministic Markov processes with boundary. ESAIM: Proceedings and Surveys, 2014, 45, pp.338-348. ⟨hal-01902024⟩
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