Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities

doi:10.1007/s00440-020-00991-w

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	Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities
	Gordina, Maria 1; Roeckner, Michael 2,3; Teplyaev, Alexander 1
	2020-08-07
发表期刊	PROBABILITY THEORY AND RELATED FIELDS
ISSN	0178-8051
页码	31
摘要	We 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.
关键词	Ornstein-Uhlenbeck process Singular perturbation Nonlinear infinite-dimensional stochastic differential equations Non-Lipschitz monotone coefficients Girsanov theorem
DOI	10.1007/s00440-020-00991-w
收录类别	SCI
语种	英语
资助项目	NSF[DMS-1613025] ; NSF[DMS-1712427] ; Simons Fellowship ; German Science Foundation (DFG)[CRC 1283]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000557118400002
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51941
专题	中国科学院数学与系统科学研究院
通讯作者	Gordina, Maria
作者单位	1.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
推荐引用方式 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.