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Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities
Gordina, Maria1; Roeckner, Michael2,3; Teplyaev, Alexander1
2020-08-07
Source PublicationPROBABILITY THEORY AND RELATED FIELDS
ISSN0178-8051
Pages31
AbstractWe consider a perturbation of a Hilbert space-valued Ornstein-Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls in the Hilbert space uniformly in time. First we introduce a new notion of generalized solutions for such equations which we call pseudo-weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation. Then we prove that their laws are absolutely continuous with respect to the law of the original Ornstein-Uhlenbeck process. In particular, we show that pseudo-weak solutions always have continuous sample paths. In addition, we obtain integrability estimates of the associated Girsanov densities. Some of our results concern non-random equations as well, while probabilistic results are new even in finite-dimensional autonomous settings.
KeywordOrnstein-Uhlenbeck process Singular perturbation Nonlinear infinite-dimensional stochastic differential equations Non-Lipschitz monotone coefficients Girsanov theorem
DOI10.1007/s00440-020-00991-w
Indexed BySCI
Language英语
Funding ProjectNSF[DMS-1613025] ; NSF[DMS-1712427] ; Simons Fellowship ; German Science Foundation (DFG)[CRC 1283]
WOS Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000557118400002
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51941
Collection中国科学院数学与系统科学研究院
Corresponding AuthorGordina, Maria
Affiliation1.Univ Connecticut, Dept Math, Storrs, CT 06269 USA
2.Bielefeld Univ, Dept Math, D-33501 Bielefeld, Germany
3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Gordina, Maria,Roeckner, Michael,Teplyaev, Alexander. Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities[J]. PROBABILITY THEORY AND RELATED FIELDS,2020:31.
APA Gordina, Maria,Roeckner, Michael,&Teplyaev, Alexander.(2020).Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities.PROBABILITY THEORY AND RELATED FIELDS,31.
MLA Gordina, Maria,et al."Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities".PROBABILITY THEORY AND RELATED FIELDS (2020):31.
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