Thinning and multilevel Monte Carlo methods for piecewise deterministic (Markov) processes with an application to a stochastic Morris–Lecar model
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Publication:3298816
DOI10.1017/APR.2019.55zbMATH Open1477.65017arXiv1812.08431OpenAlexW3023576995MaRDI QIDQ3298816
Author name not available (Why is that?)
Publication date: 16 July 2020
Published in: (Search for Journal in Brave)
Abstract: In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak error expansion for Piecewise Deterministic Markov Processes (PDMP). These estimates are the building blocks of the Multilevel Monte Carlo (MLMC) method which we study in the second part. The coupling required by MLMC is based on the thinning procedure. In the third part we apply these results to a 2-dimensional Morris-Lecar model with stochastic ion channels. In the range of our simulations the MLMC estimator outperforms the classical Monte Carlo one.
Full work available at URL: https://arxiv.org/abs/1812.08431
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