An arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: analysis of probability distribution functions
An arbitrary high order weak approximation of SDE and Malliavin Monte Carlo: analysis of probability distribution functions
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SDE 和 Malliavin Monte Carlo 的任意高阶弱逼近：概率分布函数的分析
DOI：
10.1137/17m114412x
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发表时间：
2019
影响因子：
2.9
通讯作者：
Toshihiro Yamada
中科院分区：
文献类型：
--
作者：
Toshihiro Yamada;Kenta Yamamoto;Toshihiro Yamada
利用Malliavin微积分，给出了多维Stratonovich随机微分方程组的任意高阶弱逼近格式。无论测试函数是否光滑，该方案都能有效地工作。采用一种简单的数值算法--Malliavin蒙特卡罗方法来实现该格式。数值算例说明了该方法的有效性。
This paper provides an arbitrary high order weak approximation scheme for multidimensional Stratonovich stochastic differential equations using Malliavin calculus. The scheme efficiently works whether the test function is smooth or not. The Malliavin Monte Carlo method, a simple numerical algorithm, is introduced to implement the scheme. Numerical examples illustrate the validity of the method.