关于伊托公式的评论

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Theory of Probability and its Applications Pub Date : 2024-08-14 DOI:10.1137/s0040585x97t99188x

I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev

{"title":"关于伊托公式的评论","authors":"I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev","doi":"10.1137/s0040585x97t99188x","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 69, Issue 2, Page 227-242, August 2024. <br/> In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class $L_{2,\\mathrm{loc}}(\\mathbf{R})$. Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149--169] obtained a different form of the last term in the Itô formula under the same conditions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"74 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Remark on the Itô Formula\",\"authors\":\"I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev\",\"doi\":\"10.1137/s0040585x97t99188x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Theory of Probability &Its Applications, Volume 69, Issue 2, Page 227-242, August 2024. <br/> In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class $L_{2,\\\\mathrm{loc}}(\\\\mathbf{R})$. Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149--169] obtained a different form of the last term in the Itô formula under the same conditions.\",\"PeriodicalId\":51193,\"journal\":{\"name\":\"Theory of Probability and its Applications\",\"volume\":\"74 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theory of Probability and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/s0040585x97t99188x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t99188x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 0

摘要

概率论及其应用》（Theory of Probability &Its Applications），第 69 卷，第 2 期，第 227-242 页，2024 年 8 月。在经典的伊托公式中，我们建议用分布微分意义上的二阶导数代替二阶导数（通常意义上的理解）。我们特别指出，如果一阶导数位于类$L_{2,\mathrm{loc}}(\mathbf{R})$中，就可以做到这一点。早些时候，Föllmer、Protter 和 Shiryayev [Bernoulli, 1 (1995), pp.

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

A Remark on the Itô Formula

Theory of Probability &Its Applications, Volume 69, Issue 2, Page 227-242, August 2024.
In the classical Itô formula, we propose replacing the second derivative (understood in the usual sense) by the second derivative in the sense of differentiation of distributions. In particular, we show that this can be done if the first derivative lies in the class $L_{2,\mathrm{loc}}(\mathbf{R})$. Earlier, Föllmer, Protter, and Shiryayev [Bernoulli, 1 (1995), pp. 149--169] obtained a different form of the last term in the Itô formula under the same conditions.

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

Theory of Probability and its Applications 数学-统计学与概率论

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

6 months

期刊介绍： Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.