Exact simulation of the jump times of a class of Piecewise Deterministic Markov Processes

Vincent Lemaire, Michèle Thieullen, Nicolas Thomas

Published 2016-02-25Version 1

In this paper, we extend the thinning procedure of Poisson processes to a class of Piecewise Deterministic Markov Processes (PDMPs). This allows to simulate exactly trajectories of such processes when the family of flows is known explicitly. We provide an explicit algorithm and we also extend the notion of "rate of acceptance" which is the measure of efficiency of a thinning algorithm. We characterise the point process formed by the rejected points obtained by thinning by showing that it is a Cox process. The thinning procedure provides a new way to simulate Hodgkin-Huxley models with Markovian ion channels dynamic. We also present a decomposition of the transition measure of one of these models which is numerically efficient.