Quantitative concentration of stationary measures
文献类型：期刊论文
| 作者 | Ji, Min1,4 ; Shen, Zhongwei3; Yi, Yingfei2,3
|
| 刊名 | PHYSICA D-NONLINEAR PHENOMENA
 |
| 出版日期 | 2019-12-01 |
| 卷号 | 399页码:73-85 |
| ISSN号 | 0167-2789 |
| 关键词 | Fokker-Planck equation Stationary measure Qualitative concentration Stochastic stability Lyapunov function |
| DOI | 10.1016/j.physd.2019.04.006 |
| 英文摘要 | We consider an Ito stochastic differential equation and study the asymptotic behaviors of stationary measures of the corresponding Fokker-Planck equation in the vicinity of a deterministic attractor or a repeller. By establishing global measure estimates in domains of interest, we show Gaussian-like behaviors of these measures in the basins of the attractor and the repeller. Not only do our results quantify the concentration results of stationary measures obtained in Huang et al. (2018), but also they are valid near a usual attractor (resp. repeller) instead of a strong attractor (resp. repeller) assumed in Huang et al. (2018). Our approach in conducting the measure estimates is based on a new idea of constructing a sequence of Lyapunov functions (anti-Lyapunov functions) in the basin of attraction (resp. expansion) of the attractor (resp. repeller). As applications of these measure estimates, we also derive upper bounds for the differential entropy and establish certain entropy-dimension inequalities. (C) 2019 Elsevier B.V. All rights reserved. |
| 资助项目 | NSFC[11571344] ; University of Alberta ; NSERC[1257749] ; NSERC[RGPIN-2018-04371] ; NSERC[DGECR-2018-00353] ; PIMS CRG grant ; Jilin University |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| 出版者 | ELSEVIER |
| WOS记录号 | WOS:000482872900006 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/35639]  |
| 专题 | 数学所 |
| 通讯作者 | Shen, Zhongwei |
| 作者单位 | 1.Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China 3.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 4.Univ Chinese Acad Sci, Chinese Acad Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ji, Min,Shen, Zhongwei,Yi, Yingfei. Quantitative concentration of stationary measures[J]. PHYSICA D-NONLINEAR PHENOMENA,2019,399:73-85. |
| APA | Ji, Min,Shen, Zhongwei,&Yi, Yingfei.(2019).Quantitative concentration of stationary measures.PHYSICA D-NONLINEAR PHENOMENA,399,73-85. |
| MLA | Ji, Min,et al."Quantitative concentration of stationary measures".PHYSICA D-NONLINEAR PHENOMENA 399(2019):73-85. |
入库方式： OAI收割
来源：数学与系统科学研究院
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