伯努利过程的随机分析

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2008-09-18 DOI:10.1214/08-PS139

Nicolas Privault

{"title":"伯努利过程的随机分析","authors":"Nicolas Privault","doi":"10.1214/08-PS139","DOIUrl":null,"url":null,"abstract":"These notes survey some aspects of discrete-time chaotic calculus \n and its applications, based on the chaos representation property \n for i.i.d. sequences of random variables. \n The topics covered include the Clark formula and predictable \n representation, anticipating calculus, covariance identities and \n functional inequalities (such as deviation and logarithmic Sobolev \n inequalities), and an application to option hedging in discrete time.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":"5 1","pages":"435-483"},"PeriodicalIF":1.3000,"publicationDate":"2008-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"71","resultStr":"{\"title\":\"Stochastic analysis of Bernoulli processes\",\"authors\":\"Nicolas Privault\",\"doi\":\"10.1214/08-PS139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"These notes survey some aspects of discrete-time chaotic calculus \\n and its applications, based on the chaos representation property \\n for i.i.d. sequences of random variables. \\n The topics covered include the Clark formula and predictable \\n representation, anticipating calculus, covariance identities and \\n functional inequalities (such as deviation and logarithmic Sobolev \\n inequalities), and an application to option hedging in discrete time.\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":\"5 1\",\"pages\":\"435-483\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2008-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"71\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/08-PS139\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/08-PS139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 71

摘要

这些笔记根据随机变量的i.i.d序列的混沌表示性质，综述了离散时间混沌演算的一些方面及其应用。涵盖的主题包括克拉克公式和可预测表示，预测微积分，协方差恒等式和功能不等式(如偏差和对数Sobolev不等式)，以及离散时间期权对冲的应用。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Stochastic analysis of Bernoulli processes

These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable representation, anticipating calculus, covariance identities and functional inequalities (such as deviation and logarithmic Sobolev inequalities), and an application to option hedging in discrete time.

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