A natural extension of Markov processes and applications to singular SDEs
文献类型：期刊论文
| 作者 | Beznea, Lucian1,2,3; Cimpean, Iulian1; Rockner, Michael4,5 |
| 刊名 | ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
 |
| 出版日期 | 2020-11-01 |
| 卷号 | 56期号:4页码:2480-2506 |
| 关键词 | Stochastic differential equation on Hilbert spaces Stochastic PDE Martingale problem Not allowed starting point Girsanov transform Nonregular drift Dirichlet form Right process Fine topology |
| ISSN号 | 0246-0203 |
| DOI | 10.1214/20-AIHP1047 |
| 英文摘要 | We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made stuck in the added points, and it renders a new technique of constructing extended solutions to S(P)DEs from all starting points, in such a way that they are solutions at least after any strictly positive time. Concretely, we adopt this strategy to study SDEs with singular coefficients on an infinite dimensional state space (e.g. SPDEs of evolutionary type), for which one often encounters the situation where not every point in the space is allowed as an initial condition. The same can happen when constructing solutions of martingale problems or Markov processes from (generalized) Dirichlet forms, to which our new technique also applies. |
| 资助项目 | Deutsche Forschungsgemeinschaft[CRC 1283] ; Ministry of Research and Innovation, CNCS -UEFISCDI within PNCDI III[PN-III-P4-IDPCE-2016-0372] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000582036900010 |
| 出版者 | INST MATHEMATICAL STATISTICS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52412]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Beznea, Lucian |
| 作者单位 | 1.Romanian Acad, Simion Stoilow Inst Math, Res Unit 2,POB 1-764, RO-014700 Bucharest, Romania 2.Univ Bucharest, Fac Math & Comp Sci, Bucharest, Romania 3.Ctr Francophone Math Bucarest, Bucharest, Romania 4.Univ Bielefeld, Fak Math, Postfach 100 131, D-33501 Bielefeld, Germany 5.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Beznea, Lucian,Cimpean, Iulian,Rockner, Michael. A natural extension of Markov processes and applications to singular SDEs[J]. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,2020,56(4):2480-2506. |
| APA | Beznea, Lucian,Cimpean, Iulian,&Rockner, Michael.(2020).A natural extension of Markov processes and applications to singular SDEs.ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES,56(4),2480-2506. |
| MLA | Beznea, Lucian,et al."A natural extension of Markov processes and applications to singular SDEs".ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES 56.4(2020):2480-2506. |
入库方式： OAI收割
来源：数学与系统科学研究院
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