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

Vincent Lemaire (1) , Michèle Thieullen (1) , Nicolas Thomas (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Channel noise; 65C20; 92C20; 92C45; Piecewise Deterministic Markov Process; Exact simulation; Thinning; Neural model

Domaines: Probabilités [math.PR]

Vincent Lemaire, Michèle Thieullen, Nicolas Thomas. Exact simulation of the jump times of a class of Piecewise Deterministic Markov Processes. Journal of Scientific Computing, 2017, ⟨10.1007/s10915-017-0607-4⟩. ⟨hal-01443468⟩