Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels
Operator splitting around Euler-Maruyama scheme and high order discretization of heat kernels
复制标题
围绕 Euler-Maruyama 方案的算子分裂和热核的高阶离散化
DOI：
10.1051/m2an/2020043
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Toshihiro Yamada
中科院分区：
文献类型：
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作者：
Yuga Iguchi;Toshihiro Yamada
利用非对易代数的Baker-Campbell-Hausdorff型交换子展开和Malliavin演算，提出了扩散半群的一般高阶算子分裂格式。给出了热方程或热核基本解的一种精确离散化方法，并给出了一种新的计算算法，对扩散过程的推断有一定的参考价值。该近似被认为是围绕密度的Euler-Maruyama格式的分裂。给出了扩散过程的数值算例，验证了该方法的有效性。
This paper proposes a general higher order operator splitting scheme for diffusion semigroups using the Baker–Campbell–Hausdorff type commutator expansion of non-commutative algebra and the Malliavin calculus. An accurate discretization method for the fundamental solution of heat equations or the heat kernel is introduced with a new computational algorithm which will be useful for the inference for diffusion processes. The approximation is regarded as the splitting around the Euler–Maruyama scheme for the density. Numerical examples for diffusion processes are shown to validate the proposed scheme.