Assessment of Stochastic Numerical Schemes for Stochastic Differential Equations with “White Noise” Using Itô’s Integral

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-11-09 DOI:10.3390/sym15112038
Alina Bogoi, Cătălina-Ilinca Dan, Sergiu Strătilă, Grigore Cican, Daniel-Eugeniu Crunteanu
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Abstract

Stochastic Differential Equations (SDEs) model physical phenomena dominated by stochastic processes. They represent a method for studying the dynamic evolution of a physical phenomenon, like ordinary or partial differential equations, but with an additional term called “noise” that represents a perturbing factor that cannot be attached to a classical mathematical model. In this paper, we study weak and strong convergence for six numerical schemes applied to a multiplicative noise, an additive, and a system of SDEs. The Efficient Runge–Kutta (ERK) technique, however, comes out as the top performer, displaying the best convergence features in all circumstances, including in the difficult setting of multiplicative noise. This result highlights the importance of researching cutting-edge numerical techniques built especially for stochastic systems and we consider to be of good help to the MATLAB function code for the ERK method.
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利用Itô积分评价带有“白噪声”的随机微分方程的随机数值格式
随机微分方程(SDEs)对随机过程主导的物理现象进行建模。它们代表了一种研究物理现象动态演变的方法,就像常微分方程或偏微分方程一样,但有一个额外的术语叫做“噪声”,它代表了一个不能附加到经典数学模型上的干扰因素。本文研究了六种应用于乘性噪声、加性噪声和SDEs系统的数值格式的弱收敛性和强收敛性。然而,高效龙格-库塔(ERK)技术表现最好,在所有情况下都表现出最好的收敛特征,包括在乘法噪声的困难设置中。这一结果突出了研究专门针对随机系统的前沿数值技术的重要性,我们认为这对ERK方法的MATLAB函数代码有很好的帮助。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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