Concentration and limit behaviors of stationary measures
文献类型：期刊论文
| 作者 | Huang, Wen1; Ji, Min2,3,4 ; Liu, Zhenxin5; Yi, Yingfei6,7
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| 刊名 | PHYSICA D-NONLINEAR PHENOMENA
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| 出版日期 | 2018-04-15 |
| 卷号 | 369页码:1-17 |
| 关键词 | Fokker-Planck equation Stationary measure Limit measure Concentration Stochastic stability White noise perturbation |
| ISSN号 | 0167-2789 |
| DOI | 10.1016/j.physd.2017.12.009 |
| 英文摘要 | In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative noise including additive white noise case. As the noises are vanishing, various results on the invariance and concentration of the limit measures are obtained. In particular, we show that if the noise perturbed systems admit a uniform Lyapunov function, then the stationary measures form a relatively sequentially compact set whose weak*-limits are invariant measures of the unperturbed system concentrated on its global attractor. In the case that the global attractor contains a strong local attractor, we further show that there exists a family of admissible multiplicative noises with respect to which all limit measures are actually concentrated on the local attractor; and on the contrary, in the presence of a strong local repeller in the global attractor, there exists a family of admissible multiplicative noises with respect to which no limit measure can be concentrated on the local repeller. Moreover, we show that if there is a strongly repelling equilibrium in the global attractor, then limit measures with respect to typical families of multiplicative noises are always concentrated away from the equilibrium. As applications of these results, an example of stochastic Hopf bifurcation and an example with non-decomposable omega-limit sets are provided. Our study is closely related to the problem of noise stability of compact invariant sets and invariant measures of the unperturbed system. (C) 2017 Elsevier B.V. All rights reserved. |
| 资助项目 | NSFC[11371339] ; NSFC[11431012] ; NSFC[11731003] ; NSFC[11571344] ; NSFC[11271151] ; NSFC[11522104] ; Dalian University of Technology ; NSF[DMS1109201] ; NSERC[1257749] ; University of Alberta ; Jilin University |
| WOS研究方向 | Mathematics ; Physics |
| 语种 | 英语 |
| WOS记录号 | WOS:000428831100001 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/30133]  |
| 专题 | 数学所 |
| 通讯作者 | Yi, Yingfei |
| 作者单位 | 1.Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100080, Peoples R China 4.Univ Chinese Acad Sci, Beijing 100080, Peoples R China 5.Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China 6.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 7.Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China |
| 推荐引用方式 GB/T 7714 | Huang, Wen,Ji, Min,Liu, Zhenxin,et al. Concentration and limit behaviors of stationary measures[J]. PHYSICA D-NONLINEAR PHENOMENA,2018,369:1-17. |
| APA | Huang, Wen,Ji, Min,Liu, Zhenxin,&Yi, Yingfei.(2018).Concentration and limit behaviors of stationary measures.PHYSICA D-NONLINEAR PHENOMENA,369,1-17. |
| MLA | Huang, Wen,et al."Concentration and limit behaviors of stationary measures".PHYSICA D-NONLINEAR PHENOMENA 369(2018):1-17. |
入库方式： OAI收割
来源：数学与系统科学研究院
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