KMS Of Academy of mathematics and systems sciences, CAS
| A natural extension of Markov processes and applications to singular SDEs | |
| Beznea, Lucian1,2,3; Cimpean, Iulian1; Rockner, Michael4,5 | |
| 2020-11-01 | |
| Source Publication | ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
 |
| ISSN | 0246-0203 |
| Volume | 56Issue:4Pages:2480-2506 |
| Abstract | 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. |
| Keyword | Stochastic differential equation on Hilbert spaces Stochastic PDE Martingale problem Not allowed starting point Girsanov transform Nonregular drift Dirichlet form Right process Fine topology |
| DOI | 10.1214/20-AIHP1047 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Deutsche Forschungsgemeinschaft[CRC 1283] ; Ministry of Research and Innovation, CNCS -UEFISCDI within PNCDI III[PN-III-P4-IDPCE-2016-0372] |
| WOS Research Area | Mathematics |
| WOS Subject | Statistics & Probability |
| WOS ID | WOS:000582036900010 |
| Publisher | INST MATHEMATICAL STATISTICS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52413 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Beznea, Lucian |
| Affiliation | 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 |
| Recommended Citation 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. |
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