ON SYMMETRIC LINEAR DIFFUSIONS

doi:10.1090/tran/7580

CSpace > 应用数学研究所

	ON SYMMETRIC LINEAR DIFFUSIONS
	Li, Liping1 ; Ying, Jiangang 2
	2019-04-15
发表期刊	TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9947
卷号	371 期号:8 页码:5841-5874
摘要	The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric one-dimensional diffusions, which are also called symmetric linear diffusions. Let (epsilon, F) be a regular and local Dirichlet form on L-2(I, m), where I is an interval and m is a fully supported Radon measure on I. We shall first present a complete representation for (epsilon, F), which shows that (epsilon, F) lives on at most countable disjoint "effective" intervals with an "adapted" scale function on each interval, and any point outside these intervals is a trap of the one-dimensional diffusion. Furthermore, we shall give a necessary and sufficient condition for C-c(infinity) (I) being a special standard core of (epsilon, F) and shall identify the closure of C-c(infinity) (I) in (epsilon, F) when C-c(infinity) (I) is contained but not necessarily dense in F relative to the epsilon(1/2)(1)-norm. This paper is partly motivated by a result of Hamza's that was stated in a theorem of Fukushima, Oshima, and Takeda's and that provides a different point of view to this theorem. To illustrate our results, many examples are provided.
关键词	Symmetric one-dimensional diffusions Dirichlet forms regular Dirichlet subspaces representation theorem
DOI	10.1090/tran/7580
语种	英语
资助项目	China Postdoctoral Science Foundation[2015LH0043] ; China Postdoctoral Science Foundation[2016M590145] ; Chinese Academy of Science ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences[2008DP173182]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000464034200022
出版者	AMER MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/34438
专题	应用数学研究所
通讯作者	Li, Liping
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, RCSDS, Beijing 100190, Peoples R China 2.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Li, Liping,Ying, Jiangang. ON SYMMETRIC LINEAR DIFFUSIONS[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2019,371(8):5841-5874.
APA	Li, Liping,&Ying, Jiangang.(2019).ON SYMMETRIC LINEAR DIFFUSIONS.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,371(8),5841-5874.
MLA	Li, Liping,et al."ON SYMMETRIC LINEAR DIFFUSIONS".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 371.8(2019):5841-5874.