沿随机向量场行走的单元表示和希尔伯特空间中的科尔莫戈罗夫-福克-普朗克方程

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-02-01 DOI:10.1134/s004057792402003x

{"title":"沿随机向量场行走的单元表示和希尔伯特空间中的科尔莫戈罗夫-福克-普朗克方程","authors":"","doi":"10.1134/s004057792402003x","DOIUrl":null,"url":null,"abstract":"<span> <h3>Abstract</h3> <p> Random Hamiltonian flows in an infinite-dimensional phase space is represented by random unitary groups in a Hilbert space. For this, the phase space is equipped with a measure that is invariant under a group of symplectomorphisms. The obtained representation of random flows allows applying the Chernoff averaging technique to random processes with values in the group of nonlinear operators. The properties of random unitary groups and the limit distribution for their compositions are described. </p> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unitary representation of walks along random vector fields and the Kolmogorov–Fokker–Planck equation in a Hilbert space\",\"authors\":\"\",\"doi\":\"10.1134/s004057792402003x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<span> <h3>Abstract</h3> <p> Random Hamiltonian flows in an infinite-dimensional phase space is represented by random unitary groups in a Hilbert space. For this, the phase space is equipped with a measure that is invariant under a group of symplectomorphisms. The obtained representation of random flows allows applying the Chernoff averaging technique to random processes with values in the group of nonlinear operators. The properties of random unitary groups and the limit distribution for their compositions are described. </p> </span>\",\"PeriodicalId\":797,\"journal\":{\"name\":\"Theoretical and Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1134/s004057792402003x\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s004057792402003x","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 0

摘要

摘要无穷维相空间中的随机哈密顿流由希尔伯特空间中的随机单元组表示。为此，相空间配备了一个在交映变形群下不变的度量。所获得的随机流表示法允许将切尔诺夫平均技术应用于非线性算子组中具有值的随机过程。本文还描述了随机单元群的性质及其组成的极限分布。

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

Unitary representation of walks along random vector fields and the Kolmogorov–Fokker–Planck equation in a Hilbert space

Abstract

Random Hamiltonian flows in an infinite-dimensional phase space is represented by random unitary groups in a Hilbert space. For this, the phase space is equipped with a measure that is invariant under a group of symplectomorphisms. The obtained representation of random flows allows applying the Chernoff averaging technique to random processes with values in the group of nonlinear operators. The properties of random unitary groups and the limit distribution for their compositions are described.

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

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.