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A new extrapolation method for weak approximation schemes with applications. (English) Zbl 1349.65035
Summary: 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.

MSC:
65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
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