A natural extension of Markov processes and applications to singular SDEs

doi:10.1214/20-AIHP1047

CSpace

	A natural extension of Markov processes and applications to singular SDEs
	Beznea, Lucian 1,2,3; Cimpean, Iulian 1; Rockner, Michael 4,5
	2020-11-01
发表期刊	ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES
ISSN	0246-0203
卷号	56 期号:4 页码:2480-2506
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.
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
DOI	10.1214/20-AIHP1047
收录类别	SCI
语种	英语
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
WOS类目	Statistics & Probability
WOS记录号	WOS:000582036900010
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/52413
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.