从马尔可夫过程到半鞅

IF 1.3 Q2 STATISTICS & PROBABILITY Probability Surveys Pub Date : 2022-11-28 DOI:10.1214/23-ps19
Sebastian Rickelhoff, Alexander Schnurr
{"title":"从马尔可夫过程到半鞅","authors":"Sebastian Rickelhoff, Alexander Schnurr","doi":"10.1214/23-ps19","DOIUrl":null,"url":null,"abstract":"In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the `natural' class of processes for many concepts first developed in the Markovian framework. As an example, stochastic differential equations have been invented as a tool to study Markov processes but nowadays are treated separately in the literature. Moreover, the killing of processes has been known for decades before it made its way to the theory of semimartingales most recently. We describe, when these and other important concepts have been invented in the theory of Markov processes and how they were transferred to semimartingales. Further topics include the symbol, characteristics and generalizations of Blumenthal-Getoor indices. Some additional comments on relations between Markov processes and semimartingales round out the paper.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"From Markov processes to semimartingales\",\"authors\":\"Sebastian Rickelhoff, Alexander Schnurr\",\"doi\":\"10.1214/23-ps19\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the `natural' class of processes for many concepts first developed in the Markovian framework. As an example, stochastic differential equations have been invented as a tool to study Markov processes but nowadays are treated separately in the literature. Moreover, the killing of processes has been known for decades before it made its way to the theory of semimartingales most recently. We describe, when these and other important concepts have been invented in the theory of Markov processes and how they were transferred to semimartingales. Further topics include the symbol, characteristics and generalizations of Blumenthal-Getoor indices. Some additional comments on relations between Markov processes and semimartingales round out the paper.\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-11-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ps19\",\"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/10.1214/23-ps19","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: 1

摘要

在随机积分和半鞅理论的发展中,马尔可夫过程一直是灵感的源泉。尽管这种历史交织,但对于最初在马尔可夫框架中发展起来的许多概念来说,半鞅应该被认为是“自然的”一类过程。例如,随机微分方程是作为研究马尔可夫过程的工具而发明的,但现在在文献中被单独对待。此外,在最近的半鞅理论出现之前,过程的杀戮已经被人们知道了几十年。我们描述了这些和其他重要的概念在马尔可夫过程理论中被发明的时间,以及它们是如何被转化为半鞅的。进一步的主题包括Blumenthal-Getoor指数的符号、特征和推广。对马尔可夫过程与半鞅之间的关系作了一些补充说明,使本文更加完善。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
From Markov processes to semimartingales
In the development of stochastic integration and the theory of semimartingales, Markov processes have been a constant source of inspiration. Despite this historical interweaving, it turned out that semimartingales should be considered the `natural' class of processes for many concepts first developed in the Markovian framework. As an example, stochastic differential equations have been invented as a tool to study Markov processes but nowadays are treated separately in the literature. Moreover, the killing of processes has been known for decades before it made its way to the theory of semimartingales most recently. We describe, when these and other important concepts have been invented in the theory of Markov processes and how they were transferred to semimartingales. Further topics include the symbol, characteristics and generalizations of Blumenthal-Getoor indices. Some additional comments on relations between Markov processes and semimartingales round out the paper.
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
Probability Surveys
Probability Surveys STATISTICS & PROBABILITY-
CiteScore
4.70
自引率
0.00%
发文量
9
期刊最新文献
Probabilistic representations of fragmentation equations L2-small ball asymptotics for Gaussian random functions: A survey Models of random subtrees of a graph Numerical methods for backward stochastic differential equations: A survey From Markov processes to semimartingales
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1