特定二维随机微分方程Milstein与精确耦合方法的MATLAB比较

IF 0.5 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Journal of Information Science and Engineering Pub Date : 2020-11-01 DOI:10.6688/JISE.202011_36(6).0006

Yousef Alnafisah

{"title":"特定二维随机微分方程Milstein与精确耦合方法的MATLAB比较","authors":"Yousef Alnafisah","doi":"10.6688/JISE.202011_36(6).0006","DOIUrl":null,"url":null,"abstract":"We compare Milstein and exact coupling methods for the strong approximation of solutions to stochastic differential equations (SDE), which are driven by Brownian motion. Both of these methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the exact coupling method. We also compare their implementation using MATLAB. A particular two-dimensional SDE is used in the implementation for comparing their results. Moreover, the performance of both methods and the amount of time required to obtain the result are also analyzed. It is interesting to mention that this comparison is very important in several areas, such as stochastic analysis, financial mathematics and some physical applications.","PeriodicalId":50177,"journal":{"name":"Journal of Information Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Comparison Between Milstein and Exact Coupling Methods using MATLAB for a Particular Two-Dimensional Stochastic Differential Equation\",\"authors\":\"Yousef Alnafisah\",\"doi\":\"10.6688/JISE.202011_36(6).0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We compare Milstein and exact coupling methods for the strong approximation of solutions to stochastic differential equations (SDE), which are driven by Brownian motion. Both of these methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the exact coupling method. We also compare their implementation using MATLAB. A particular two-dimensional SDE is used in the implementation for comparing their results. Moreover, the performance of both methods and the amount of time required to obtain the result are also analyzed. It is interesting to mention that this comparison is very important in several areas, such as stochastic analysis, financial mathematics and some physical applications.\",\"PeriodicalId\":50177,\"journal\":{\"name\":\"Journal of Information Science and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2020-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Information Science and Engineering\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.6688/JISE.202011_36(6).0006\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INFORMATION SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Information Science and Engineering","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.6688/JISE.202011_36(6).0006","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INFORMATION SYSTEMS","Score":null,"Total":0}

引用次数: 0

摘要

我们比较了米尔斯坦和精确耦合方法对布朗运动驱动的随机微分方程(SDE)强逼近解的求解。在精确耦合方法的扩散项不退化的假设下，这两种方法都达到了一阶收敛。我们还比较了它们在MATLAB中的实现。在实现中使用一个特定的二维SDE来比较它们的结果。此外，还分析了两种方法的性能和获得结果所需的时间。有趣的是，这种比较在一些领域是非常重要的，比如随机分析、金融数学和一些物理应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Comparison Between Milstein and Exact Coupling Methods using MATLAB for a Particular Two-Dimensional Stochastic Differential Equation

We compare Milstein and exact coupling methods for the strong approximation of solutions to stochastic differential equations (SDE), which are driven by Brownian motion. Both of these methods attain an order one convergence under the nondegeneracy assumption of the diffusion term for the exact coupling method. We also compare their implementation using MATLAB. A particular two-dimensional SDE is used in the implementation for comparing their results. Moreover, the performance of both methods and the amount of time required to obtain the result are also analyzed. It is interesting to mention that this comparison is very important in several areas, such as stochastic analysis, financial mathematics and some physical applications.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Information Science and Engineering 工程技术-计算机：信息系统

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

8 months

期刊介绍： The Journal of Information Science and Engineering is dedicated to the dissemination of information on computer science, computer engineering, and computer systems. This journal encourages articles on original research in the areas of computer hardware, software, man-machine interface, theory and applications. tutorial papers in the above-mentioned areas, and state-of-the-art papers on various aspects of computer systems and applications.