The Annals of Applied Probability

A new extrapolation method for weak approximation schemes with applications

Kojiro Oshima, Josef Teichmann, and Dejan Velušček

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Abstract

Fujiwara’s method can be considered as an extrapolation method of order 6 of the Ninomiya–Victoir weak approximation scheme for the numerical approximation of solution processes of SDEs. We present an extension of Fujiwara’s method for arbitrarily high orders, which embeds the original Fujiwara method as the order 6 case. The approach can be considered as a variant of Richardson extrapolation, which allows one to reach high orders with few extrapolation steps. The most important contribution of our approach is that we only need m extrpolation steps in order to achieve order of approximation 2m, which is half the number of steps in comparison to classical approaches.

Article information

Source
Ann. Appl. Probab., Volume 22, Number 3 (2012), 1008-1045.

Dates
First available in Project Euclid: 18 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1337347537

Digital Object Identifier
doi:10.1214/11-AAP774

Mathematical Reviews number (MathSciNet)
MR2977984

Zentralblatt MATH identifier
1349.65035

Subjects
Primary: 65H35
Secondary: 65C30: Stochastic differential and integral equations

Keywords
Weak approximation schemes high order methods cubature methods extrapolation Ninomiya–Victoir scheme Fujiwara extrapolation method Richardson extrapolation

Citation

Oshima, Kojiro; Teichmann, Josef; Velušček, Dejan. A new extrapolation method for weak approximation schemes with applications. Ann. Appl. Probab. 22 (2012), no. 3, 1008--1045. doi:10.1214/11-AAP774. https://projecteuclid.org/euclid.aoap/1337347537


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