Open Access
June 2012 A new extrapolation method for weak approximation schemes with applications
Kojiro Oshima, Josef Teichmann, Dejan Velušček
Ann. Appl. Probab. 22(3): 1008-1045 (June 2012). DOI: 10.1214/11-AAP774


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.


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Kojiro Oshima. Josef Teichmann. Dejan Velušček. "A new extrapolation method for weak approximation schemes with applications." Ann. Appl. Probab. 22 (3) 1008 - 1045, June 2012.


Published: June 2012
First available in Project Euclid: 18 May 2012

zbMATH: 1349.65035
MathSciNet: MR2977984
Digital Object Identifier: 10.1214/11-AAP774

Primary: 65H35
Secondary: 65C30

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

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.22 • No. 3 • June 2012
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