Simplified order 4.0 weak Taylor schemes for additive noise |
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Authors: | A Tocino |
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Institution: | Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced, 1. 37008-Salamanca, Spain |
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Abstract: | Following Kloeden and Platen P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992] Taylor schemes are considered here as the starting point to obtain simplified Taylor schemes replacing the multiple integrals by simpler variables. The conditions that a group of variables has to fulfill so that the new scheme reaches weak-order 4.0 in the additive noise case are given explicitly, as well as the way to find such groups. For a particular selection, a pair of stochastic schemes with order 4.0 in the weak sense, correcting the one proposed in P.E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992], is obtained. |
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Keywords: | 60H10 65C20 93E03 |
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