论文标题
ITO SDE的实施强订单的强订单方法0.5、1.0、1.5、2.0、2.5和3.0，基于统一的Taylor-Ito和Taylor-Stratonovich扩展，具有非交通噪声的ITO SDE和多个傅立叶级别的噪声
Implementation of Strong Numerical Methods of Orders 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 for Ito SDEs with Non-Commutative Noise Based on the Unified Taylor-Ito and Taylor-Stratonovich Expansions and Multiple Fourier-Legendre Series
论文作者
论文摘要
本文专门用于实施具有收敛订单的强数值方法，$ 0.5，$ 1.0，$ 1.5，$ 2.0，$ 2.5，$ 2.5，$和$ 3.0 $，用于ITO随机微分方程，具有基于UnifieD Taylor-Ito-Ito-Ito-Ito-Ito-Ito-Ito-Ito-Ito-Ito-Ito-itto-Stratonovich-stratonovich-Speastions and forey-serseions and forreier-reforder-reforder-refore-forrecord torre-forecriend-tree-forecriend和多维噪声。构建了用于实现这些方法的算法，并介绍了Python编程语言中的程序包。该软件包的重要部分，涉及迭代的ITO和Stratonovich随机积分的均值1至6的随机积分，相对于多维Wiener过程的组件，基于广义多傅立叶级数的方法。更准确地说，我们使用了Hilbert Space $ L_2（[T，T]^K）$ $ $（k = 1，\ ldots，6）$的多个傅里叶 - legendre系列，用于迭代的ITO和Stratonovich Stratonovich Stochastic积分的平均值近似。
The article is devoted to the implementation of strong numerical methods with convergence orders $0.5,$ $1.0,$ $1.5,$ $2.0,$ $2.5,$ and $3.0$ for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified Taylor--Ito and Taylor-Stratonovich expansions and multiple Fourier-Legendre series. Algorithms for the implementation of these methods are constructed and a package of programs in the Python programming language is presented. An important part of this software package, concerning the mean-square approximation of iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 with respect to components of the multidimensional Wiener process is based on the method of generalized multiple Fourier series. More precisely, we used the multiple Fourier-Legendre series converging in the sense of norm in Hilbert space $L_2([t, T]^k)$ $(k=1,\ldots,6)$ for the mean-square approximation of iterated Ito and Stratonovich stochastic integrals.
