Ninomiya-Victoir scheme : Multilevel Monte Carlo estimators and discretization of the involved Ordinary Differential Equations

Abstract : In this paper, we recall the result about the strong convergence rate of the Ninomiya-Victoir scheme and the properties of the multilevel Monte Carlo estimators involving this scheme that we introduced and studied in [2]. We are also interested in the error introduced by discretizing the ordinary differential equations involved in the Ninomiya-Victoir scheme. We prove that this error converges with strong order 2 when an explicit Runge-Kutta method with order 4 (resp. 2) is used for the ODEs corresponding to the Brownian (resp. Stratonovich drift) vector fields. We thus relax the order 5 needed in [11] for the Brownian ODEs to obtain the same order of strong convergence. Moreover, the properties of our multilevel Monte-Carlo estimators are preserved when these Runge-Kutta methods are used.
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https://hal.archives-ouvertes.fr/hal-01772609
Contributor : Emmanuelle Clément <>
Submitted on : Friday, April 20, 2018 - 2:23:32 PM
Last modification on : Monday, July 9, 2018 - 10:32:19 AM

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Emmanuelle Clément, Anis Al Gerbi, Benjamin Jourdain. Ninomiya-Victoir scheme : Multilevel Monte Carlo estimators and discretization of the involved Ordinary Differential Equations. ESAIM: Proceedings and Surveys, EDP Sciences, 2017, 59, pp.1 - 14. ⟨https://www.esaim-proc.org/articles/proc/abs/2017/04/proc175901/proc175901.html⟩. ⟨10.1051/proc/201759001⟩. ⟨hal-01772609⟩

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