A new extrapolation method for weak approximation schemes with applications
| Autor: | Kojiro Oshima, Josef Teichmann, Dejan Velušček |
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| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
Richardson extrapolation Fujiwara extrapolation method extrapolation Extrapolation Weak approximation schemes Mathematics::Numerical Analysis Numerical approximation FOS: Mathematics 65C30 Applied mathematics Mathematics - Numerical Analysis Mathematics 65H35 cubature methods Probability (math.PR) Mathematical analysis Order (ring theory) Numerical Analysis (math.NA) Extension (predicate logic) high order methods Scheme (mathematics) Ninomiya–Victoir scheme Statistics Probability and Uncertainty Mathematics - Probability |
| Zdroj: | Ann. Appl. Probab. 22, no. 3 (2012), 1008-1045 |
| ISSN: | 1050-5164 |
| DOI: | 10.1214/11-aap774 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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