蒙特卡罗方法误差表达式中常数的选择

Pub Date : 2024-04-24 DOI:10.1515/mcma-2024-2004
Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek
{"title":"蒙特卡罗方法误差表达式中常数的选择","authors":"Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek","doi":"10.1515/mcma-2024-2004","DOIUrl":null,"url":null,"abstract":"\n <jats:p>This paper considers three approaches to choosing the constant <jats:italic>H</jats:italic> in the expression <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9999\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mrow>\n <m:mi>H</m:mi>\n <m:mo>⁢</m:mo>\n <m:msqrt>\n <m:mrow>\n <m:mi>𝐃</m:mi>\n <m:mo>⁢</m:mo>\n <m:mi>ζ</m:mi>\n </m:mrow>\n </m:msqrt>\n </m:mrow>\n <m:mo>/</m:mo>\n <m:msqrt>\n <m:mi>n</m:mi>\n </m:msqrt>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_mcma-2024-2004_eq_0044.png\" />\n <jats:tex-math>{H\\sqrt{{\\mathbf{D}}\\zeta}/\\sqrt{n}}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> for the error of the Monte Carlo method for numerical calculation of mathematical expectation <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9998\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mi>𝐄</m:mi>\n <m:mo>⁢</m:mo>\n <m:mi>ζ</m:mi>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_mcma-2024-2004_eq_0114.png\" />\n <jats:tex-math>{{\\mathbf{E}}\\zeta}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula> of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9997\">\n <jats:alternatives>\n <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\n <m:mrow>\n <m:mi>H</m:mi>\n <m:mo>=</m:mo>\n <m:msqrt>\n <m:mfrac>\n <m:mn>2</m:mn>\n <m:mi>π</m:mi>\n </m:mfrac>\n </m:msqrt>\n <m:mo>=</m:mo>\n <m:mrow>\n <m:mn>0.79788456079</m:mn>\n <m:mo>⁢</m:mo>\n <m:mi mathvariant=\"normal\">…</m:mi>\n </m:mrow>\n </m:mrow>\n </m:math>\n <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_mcma-2024-2004_eq_0043.png\" />\n <jats:tex-math>{H=\\sqrt{\\frac{2}{\\pi}}=0.79788456079\\dots}</jats:tex-math>\n </jats:alternatives>\n </jats:inline-formula>  .</jats:p>","PeriodicalId":0,"journal":{"name":"","volume":"60 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Choice of a constant in the expression for the error of the Monte Carlo method\",\"authors\":\"Viktor Bryzgalov, Nurlibay Shlimbetov, Anton Voytishek\",\"doi\":\"10.1515/mcma-2024-2004\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n <jats:p>This paper considers three approaches to choosing the constant <jats:italic>H</jats:italic> in the expression <jats:inline-formula id=\\\"j_mcma-2024-2004_ineq_9999\\\">\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:mrow>\\n <m:mrow>\\n <m:mi>H</m:mi>\\n <m:mo>⁢</m:mo>\\n <m:msqrt>\\n <m:mrow>\\n <m:mi>𝐃</m:mi>\\n <m:mo>⁢</m:mo>\\n <m:mi>ζ</m:mi>\\n </m:mrow>\\n </m:msqrt>\\n </m:mrow>\\n <m:mo>/</m:mo>\\n <m:msqrt>\\n <m:mi>n</m:mi>\\n </m:msqrt>\\n </m:mrow>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_mcma-2024-2004_eq_0044.png\\\" />\\n <jats:tex-math>{H\\\\sqrt{{\\\\mathbf{D}}\\\\zeta}/\\\\sqrt{n}}</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula> for the error of the Monte Carlo method for numerical calculation of mathematical expectation <jats:inline-formula id=\\\"j_mcma-2024-2004_ineq_9998\\\">\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:mrow>\\n <m:mi>𝐄</m:mi>\\n <m:mo>⁢</m:mo>\\n <m:mi>ζ</m:mi>\\n </m:mrow>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_mcma-2024-2004_eq_0114.png\\\" />\\n <jats:tex-math>{{\\\\mathbf{E}}\\\\zeta}</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula> of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant <jats:inline-formula id=\\\"j_mcma-2024-2004_ineq_9997\\\">\\n <jats:alternatives>\\n <m:math xmlns:m=\\\"http://www.w3.org/1998/Math/MathML\\\">\\n <m:mrow>\\n <m:mi>H</m:mi>\\n <m:mo>=</m:mo>\\n <m:msqrt>\\n <m:mfrac>\\n <m:mn>2</m:mn>\\n <m:mi>π</m:mi>\\n </m:mfrac>\\n </m:msqrt>\\n <m:mo>=</m:mo>\\n <m:mrow>\\n <m:mn>0.79788456079</m:mn>\\n <m:mo>⁢</m:mo>\\n <m:mi mathvariant=\\\"normal\\\">…</m:mi>\\n </m:mrow>\\n </m:mrow>\\n </m:math>\\n <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" xlink:href=\\\"graphic/j_mcma-2024-2004_eq_0043.png\\\" />\\n <jats:tex-math>{H=\\\\sqrt{\\\\frac{2}{\\\\pi}}=0.79788456079\\\\dots}</jats:tex-math>\\n </jats:alternatives>\\n </jats:inline-formula>  .</jats:p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":\"60 7\",\"pages\":\"\"},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/mcma-2024-2004\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/mcma-2024-2004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

This paper considers three approaches to choosing the constant H in the expression H ⁢ 𝐃 ⁢ ζ / n {H\sqrt{{\mathbf{D}}\zeta}/\sqrt{n}} for the error of the Monte Carlo method for numerical calculation of mathematical expectation 𝐄 ⁢ ζ {{\mathbf{E}}\zeta} of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant H = 2 π = 0.79788456079 ⁢ … {H=\sqrt{\frac{2}{\pi}}=0.79788456079\dots}   .
本文章由计算机程序翻译,如有差异,请以英文原文为准。
分享
查看原文
Choice of a constant in the expression for the error of the Monte Carlo method
This paper considers three approaches to choosing the constant H in the expression H 𝐃 ζ / n {H\sqrt{{\mathbf{D}}\zeta}/\sqrt{n}} for the error of the Monte Carlo method for numerical calculation of mathematical expectation 𝐄 ζ {{\mathbf{E}}\zeta} of a random variable ζ: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the “in mean” approach with the constant H = 2 π = 0.79788456079 {H=\sqrt{\frac{2}{\pi}}=0.79788456079\dots}   .
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
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信