用龙格-库塔法对白噪声微分方程进行数字仿真

Hangju Cho
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引用次数: 0

摘要

本文研究了几种基于经典龙格-库塔公式的白噪声驱动微分方程数值模拟的数值积分方法。因此,我们证明了Riggs和Phillips近似(1987)的n阶矩收敛于Ito方程解的n阶矩,这与标准Runge Kutta方法的情况相反。因此,在使用Riggs和Phillips方法进行数字仿真之前,必须将白噪声微分方程转换为等效的Ito方程。提出了一种改进的里格斯和菲利普斯方法。
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Digital simulation of white noise differential equations using Runge Kutta method
In this paper we study some numerical integration methods based on the classical Runge Kutta formula for the digital simulation of differential equations driven by white noise. As a result, we show that the n-th moments of the Riggs and Phillips approximations (1987) converge to those of the solution of Ito equation, which is in contrast to the case of the standard Runge Kutta method. Therefore we must convert the white noise differential equations into the equivalent Ito equations before we use the Riggs and Phillips method for digital simulation. An improved version of the Riggs and Phillips method is also presented.
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