Thinning and Multilevel Monte Carlo for Piecewise Deterministic (Markov) Processes. Application to a stochastic Morris-Lecar model

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.
Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01960702
Contributeur : Nicolas Thomas <>
Soumis le : mercredi 19 décembre 2018 - 15:14:32
Dernière modification le : mardi 19 mars 2019 - 01:23:32
Document(s) archivé(s) le : mercredi 20 mars 2019 - 22:55:04

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  • HAL Id : hal-01960702, version 1
  • ARXIV : 1812.08431

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Vincent Lemaire, Michèle Thieullen, Nicolas Thomas. Thinning and Multilevel Monte Carlo for Piecewise Deterministic (Markov) Processes. Application to a stochastic Morris-Lecar model. 2018. 〈hal-01960702〉

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