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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.
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https://hal.archives-ouvertes.fr/hal-01960702
Contributor : Nicolas Thomas <>
Submitted on : Wednesday, December 19, 2018 - 3:14:32 PM
Last modification on : Friday, April 10, 2020 - 5:26:47 PM
Document(s) archivé(s) le : Wednesday, March 20, 2019 - 10:55:04 PM

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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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