Effective intervals and regular Dirichlet subspaces

doi:10.1016/j.spa.2020.05.003

CSpace > 应用数学研究所

	Effective intervals and regular Dirichlet subspaces
	Li, Liping1 ; Sun, Wenjie 2,3; Ying, Jiangang 4
	2020-10-01
发表期刊	STOCHASTIC PROCESSES AND THEIR APPLICATIONS
ISSN	0304-4149
卷号	130 期号:10 页码:6064-6093
摘要	It is shown in Li and Ying (2019) that a regular and local Dirichlet form on an interval can be represented by so-called effective intervals with scale functions. This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces. The first result is a complete characterization for a Dirichlet form to be a regular subspace of such a Dirichlet form in terms of effective intervals. Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in the representation above. Finally applying previous results, we shall prove that every regular and local Dirichlet form has a special standard core generated by a continuous and strictly increasing function. (C) 2020 Elsevier B.V. All rights reserved.
关键词	Dirichlet forms Regular Dirichlet subspaces One-dimensional symmetric diffusions Scale functions
DOI	10.1016/j.spa.2020.05.003
收录类别	SCI
语种	英语
资助项目	NSFC[11871162] ; NSFC[11688101] ; NSFC[11801546] ; NSFC[11931004] ; Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences[2008DP173182] ; National Postdoctoral Program for Innovative Talents of China[BX20190357]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000562734000007
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52028
专题	应用数学研究所
通讯作者	Sun, Wenjie
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, RCSDS, Beijing 100190, Peoples R China 2.Fudan Univ, Shanghai Ctr Math Sci, Shanghai 200433, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China 4.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Li, Liping,Sun, Wenjie,Ying, Jiangang. Effective intervals and regular Dirichlet subspaces[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS,2020,130(10):6064-6093.
APA	Li, Liping,Sun, Wenjie,&Ying, Jiangang.(2020).Effective intervals and regular Dirichlet subspaces.STOCHASTIC PROCESSES AND THEIR APPLICATIONS,130(10),6064-6093.
MLA	Li, Liping,et al."Effective intervals and regular Dirichlet subspaces".STOCHASTIC PROCESSES AND THEIR APPLICATIONS 130.10(2020):6064-6093.