Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities
文献类型：期刊论文
| 作者 | Gordina, Maria2; Roeckner, Michael1,3; Teplyaev, Alexander2 |
| 刊名 | PROBABILITY THEORY AND RELATED FIELDS
 |
| 出版日期 | 2020-08-07 |
| 页码 | 31 |
| ISSN号 | 0178-8051 |
| 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 |
| 英文摘要 | 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. |
| 资助项目 | NSF[DMS-1613025] ; NSF[DMS-1712427] ; Simons Fellowship ; German Science Foundation (DFG)[CRC 1283] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | SPRINGER HEIDELBERG |
| WOS记录号 | WOS:000557118400002 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51940]  |
| 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.Bielefeld Univ, Dept Math, D-33501 Bielefeld, Germany 2.Univ Connecticut, Dept Math, Storrs, CT 06269 USA 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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