Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
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DOI：
10.1007/s10543-010-0276-2
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发表时间：
2010-09-01
影响因子：
1.5
通讯作者：
Debrabant, Kristian
中科院分区：
文献类型：
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作者：
Debrabant, Kristian
提出了一类新的求解带加性噪声随机微分方程的三阶Runge-Kutta方法。与Platen的方法相比，据作者所知，这是迄今为止唯一已知的三阶Runge-Kutta弱近似方法，新的一类方法提供了更少的随机变量评估，也适用于具有多维噪声的SDES。计算了直至三阶的阶次条件，并给出了四阶段三阶方法的系数。该方法具有确定性的四阶和最小的误差常数，并且比Platen方法需要更少的函数求值。应用于一些例子，新的方法进行了比较数值与Platen的方法和一些著名的二阶方法，并产生非常有前途的结果。
A new class of third order Runge-Kutta methods for stochastic differential equations with additive noise is introduced. In contrast to Platen's method, which to the knowledge of the author has been up to now the only known third order Runge-Kutta scheme for weak approximation, the new class of methods affords less random variable evaluations and is also applicable to SDEs with multidimensional noise. Order conditions up to order three are calculated and coefficients of a four stage third order method are given. This method has deterministic order four and minimized error constants, and needs in addition less function evaluations than the method of Platen. Applied to some examples, the new method is compared numerically with Platen's method and some well known second order methods and yields very promising results.