Towards mesoscopic ergodic theory
文献类型：期刊论文
| 作者 | Qi, Weiwei1,3,4; Shen, Zhongwei1; Wang, Shirou1; Yi, Yingfei1,2 |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2020-08-10 |
| 页码 | 24 |
| ISSN号 | 1674-7283 |
| 关键词 | ergodic theory stochastic differential equation Fokker-Planck equation stationary measure physical measure mesoscopic limit |
| DOI | 10.1007/s11425-019-1642-5 |
| 英文摘要 | The present paper is devoted to a preliminary study towards the establishment of an ergodic theory for stochastic differential equations (SDEs) with less regular coefficients and degenerate noises. These equations are often derived as mesoscopic limits of complex or huge microscopic systems. By studying the associated Fokker-Planck equation (FPE), we prove the convergence of the time average of globally defined weak solutions of such an SDE to the set of stationary measures of the FPE under Lyapunov conditions. In the case where the set of stationary measures consists of a single element, the unique stationary measure is shown to be physical. Similar convergence results for the solutions of the FPE are established as well. Some of our convergence results, while being special cases of those contained in Ji et al. (2019) for SDEs with periodic coefficients, have weaken the required Lyapunov conditions and are of much simplified proofs. Applications to stochastic damping Hamiltonian systems and stochastic slow-fast systems are given. |
| 资助项目 | China Scholarship Council ; University of Alberta ; Natural Sciences and Engineering Research Council of Canada[RGPIN-2018-04371] ; Natural Sciences and Engineering Research Council of Canada[DGECR-2018-00353] ; Pacific Institute for the Mathematical Sciences-Canadian Statistical Sciences Institute Postdoctoral Fellowship ; Pacific Institute for the Mathematical Sciences-Collaborative Research Group Grant ; National Natural Science Foundation of China[11771026] ; National Natural Science Foundation of China[11471344] ; Pacific Institute for the Mathematical Sciences-University of Washington site through National Science Foundation of USA[DMS-1712701] ; Natural Sciences and Engineering Research Council of Canada Discovery[1257749] ; Jilin University |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| 出版者 | SCIENCE PRESS |
| WOS记录号 | WOS:000558872800001 |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/51985]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Yi, Yingfei |
| 作者单位 | 1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 2.Jilin Univ, Sch Math, Changchun 130012, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Qi, Weiwei,Shen, Zhongwei,Wang, Shirou,et al. Towards mesoscopic ergodic theory[J]. SCIENCE CHINA-MATHEMATICS,2020:24. |
| APA | Qi, Weiwei,Shen, Zhongwei,Wang, Shirou,&Yi, Yingfei.(2020).Towards mesoscopic ergodic theory.SCIENCE CHINA-MATHEMATICS,24. |
| MLA | Qi, Weiwei,et al."Towards mesoscopic ergodic theory".SCIENCE CHINA-MATHEMATICS (2020):24. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。