Regular Dirichlet extensions of one-dimensional Brownian motion

doi:10.1214/18-AIHP935

CSpace > 应用数学研究所

	Regular Dirichlet extensions of one-dimensional Brownian motion
	Li, Liping1 ; Ying, Jiangang 2
	2019-11-01
发表期刊	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN	0246-0203
卷号	55 期号:4 页码:1815-1849
摘要	The regular Dirichlet extension is the dual concept of regular Dirichlet subspace. The main purpose of this paper is to characterize all the regular Dirichlet extensions of one-dimensional Brownian motion and to explore their structures. It is shown that every regular Dirichlet extension of one-dimensional Brownian motion may essentially decomposed into at most countable disjoint invariant intervals and an epsilon-polar set relative to this regular Dirichlet extension. On each invariant interval the regular Dirichlet extension is characterized uniquely by a scale function in a given class. To explore the structure of regular Dirichlet extension we apply the idea introduced in (Ann. Probab. 45 (2017) 857-872), we formulate the trace Dirichlet forms and attain the darning process associated with the restriction to each invariant interval of the orthogonal complement of H-e(1)(R) in the extended Dirichlet space of the regular Dirichlet extension. As a result, we find an answer to a long-standing problem whether a pure jump Dirichlet form has proper regular Dirichlet subspaces.
关键词	Regular Dirichlet extensions Regular Dirichlet subspaces Trace Dirichlet forms Diffusion processes
DOI	10.1214/18-AIHP935
收录类别	SCI
语种	英语
资助项目	NSFC[11688101] ; NSFC[11801546] ; NSFC[11271240] ; China Postdoctoral Science Foundation[2015LH0043] ; China Postdoctoral Science Foundation[2016M590145] ; Chinese Academy of Science[2015LH0043] ; Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000496132400001
出版者	INST MATHEMATICAL STATISTICS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50652
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, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Li, Liping,Ying, Jiangang. Regular Dirichlet extensions of one-dimensional Brownian motion[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2019,55(4):1815-1849.
APA	Li, Liping,&Ying, Jiangang.(2019).Regular Dirichlet extensions of one-dimensional Brownian motion.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,55(4),1815-1849.
MLA	Li, Liping,et al."Regular Dirichlet extensions of one-dimensional Brownian motion".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 55.4(2019):1815-1849.