论文标题
Taylor-Ito和Taylor-Stratonovich扩展的四种新形式及其应用于ITO随机微分方程的高阶强数值方法
Four New Forms of the Taylor-Ito and Taylor-Stratonovich Expansions and its Application to the High-Order Strong Numerical Methods for Ito Stochastic Differential Equations
论文作者
论文摘要
在固定时刻的附近，ITO随机过程的Taylor-Ito和Taylor-Statonovich扩展的问题被考虑。 Taylor-Ito和Taylor-Stratonovich扩展的经典形式转化为四个新表示，其中包括不同类型的Iterated Ito和Stratonovich随机积分的最小组。因此，这些表示形式（所谓的统一的泰勒-Ito和Taylor-Stratonovich扩展）更方便地构建用于ITO随机微分方程的高阶强数值方法。基于统一的Taylor-Ito和Taylor-Stratonovich的扩展，具有收敛1.0、1.5、2.0、2.5和3.0的顺序的显式一步强数值方案。来自这些数值方案的迭代ITO和Stratonovich随机积分的有效均方根近似是在具有多重性1至6的多个傅立叶 - legendre系列的基础上构建的。
The problem of the Taylor-Ito and Taylor-Stratonovich expansions of the Ito stochastic processes in a neighborhood of a fixed moment of time is considered. The classical forms of the Taylor-Ito and Taylor-Stratonovich expansions are transformed to the four new representations, which includes the minimal sets of different types of iterated Ito and Stratonovich stochastic integrals. Therefore, these representations (the so-called unified Taylor-Ito and Taylor-Stratonovich expansions) are more convenient for constructing of high-order strong numerical methods for Ito stochastic differential equations. Explicit one-step strong numerical schemes with the orders of convergence 1.0, 1.5, 2.0, 2.5, and 3.0 based on the unified Taylor-Ito and Taylor-Stratonovich expansions are derived. Effective mean-square approximations of iterated Ito and Stratonovich stochastic integrals from these numerical schemes are constructed on the base of the multiple Fourier-Legendre series with multiplicities 1 to 6.
