A finite difference method for piecewise deterministic Markov processes
Numerical Analysis
2025-10-20 v4 Numerical Analysis
Abstract
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding Liouville-Master Equation is established and the upwind method is applied to numerical calculation of the distribution function. The convergence of the numerical solution is proved under an appropriate Courant-Friedrichs-Lewy condition. The same condition preserve the non-decreasing property of the calculated distribution function. Some numerical tests are presented.
Cite
@article{arxiv.math/0606588,
title = {A finite difference method for piecewise deterministic Markov processes},
author = {Mario Annunziato},
journal= {arXiv preprint arXiv:math/0606588},
year = {2025}
}
Comments
12 pages, 2 figures, submitted to Elsevier