Regular Dirichlet extensions of one-dimensional Brownian motion
文献类型：期刊论文
| 作者 | Li, Liping2 ; Ying, Jiangang1
|
| 刊名 | ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
 |
| 出版日期 | 2019-11-01 |
| 卷号 | 55期号:4页码:1815-1849 |
| 关键词 | Regular Dirichlet extensions Regular Dirichlet subspaces Trace Dirichlet forms Diffusion processes |
| ISSN号 | 0246-0203 |
| DOI | 10.1214/18-AIHP935 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000496132400001 |
| 出版者 | INST MATHEMATICAL STATISTICS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50651]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Li, Liping |
| 作者单位 | 1.Fudan Univ, Shanghai 200433, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, RCSDS, Beijing 100190, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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