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

DOI10.1051/proc/201759001zbMath1384.65042arXiv1612.07017OpenAlexW2767465718MaRDI QIDQ4606416

Benjamin Jourdain, Anis Al Gerbi, Emmanuelle Clément

Publication date: 7 March 2018

Published in: ESAIM: Proceedings and Surveys (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07017

zbMATH Keywords

convergenceRunge-Kutta methodNinomiya-Victoir schemeBrownian vector fieldsmultilevel Monte Carlo estimators

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (1)

An asymptotic radius of convergence for the Loewner equation and simulation of \(\mathrm{SLE}_{\kappa}\) traces via splitting

Cites Work

• Approximation of Markov semigroups in total variation distance
• Ninomiya-Victoir scheme: strong convergence, antithetic version and application to multilevel estimators
• A new extrapolation method for weak approximation schemes with applications
• A new higher-order weak approximation scheme for stochastic differential equations and the Runge-Kutta method
• Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation
• On the Acceleration of the Multi-Level Monte Carlo Method
• Multilevel Monte Carlo Path Simulation
• Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing
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