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Journal of Scientific Computing

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02-12-2017

Exact Simulation of the Jump Times of a Class of Piecewise Deterministic Markov Processes

Authors: Vincent Lemaire, Michèle Thieullen, Nicolas Thomas

Published in: Journal of Scientific Computing | Issue 3/2018

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Abstract

In this paper, we are interested in the exact simulation of a class of piecewise deterministic Markov processes. We show how to perform an efficient thinning algorithm depending on the jump rate bound. For different types of bounds, we compare theoretically the efficiency of the algorithm (measured by the mean ratio between the total number of jump times generated by thinning and the number of selected ones) and we compare numerically the computation times. We use the thinning algorithm on Hodgkin–Huxley models with Markovian ion channels dynamics to illustrate our results.

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Title: Exact Simulation of the Jump Times of a Class of Piecewise Deterministic Markov Processes
Authors: Vincent Lemaire
Michèle Thieullen
Nicolas Thomas
Publication date: 02-12-2017
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2018
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-017-0607-4

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