Numerical methods for piecewise deterministic Markov processes with boundary
Abstract
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.
Cite
@article{arxiv.1810.10215,
title = {Numerical methods for piecewise deterministic Markov processes with boundary},
author = {Ludovic Goudenège},
journal= {arXiv preprint arXiv:1810.10215},
year = {2018}
}