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

TL;DR

This paper presents methods for the exact simulation of certain PDMPs using thinning algorithms, comparing their efficiency and jump time statistics, with applications to Hodgkin-Huxley models.

Contribution

It introduces efficient thinning algorithms for simulating PDMPs with different jump rate bounds and compares their theoretical and numerical performance.

Findings

Thinning algorithms' efficiency varies with jump rate bounds.

Theoretical comparison of mean jump times for different bounds.

Numerical results demonstrate simulation time differences.

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.