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

Abstract

In this paper, we are interested in the exact simulation of a class of Piecewise Deterministic Markov Processes (PDMP). We show how to perform efficient thinning algorithms depending on the jump rate bound. For different types of jump rate bounds, we compare theoretically the mean number of generated (total) jump times and we compare numerically the simulation times. We use thinning algorithms on Hodgkin-Huxley models with Markovian ion channels dynamic to illustrate the results.

32 pages, 6 figures

References in corpus (3)

• On stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons
• Stochastic Representations of Ion Channel Kinetics and Exact Stochastic Simulation of Neuronal Dynamics
• Quantitative speeds of convergence for exposure to food contaminants

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