KMS Of Academy of mathematics and systems sciences, CAS
| Towards mesoscopic ergodic theory | |
| Qi, Weiwei1,2,3; Shen, Zhongwei3; Wang, Shirou3; Yi, Yingfei3,4 | |
| 2020-08-10 | |
| Source Publication | SCIENCE CHINA-MATHEMATICS
 |
| ISSN | 1674-7283 |
| Pages | 24 |
| Abstract | 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. |
| Keyword | ergodic theory stochastic differential equation Fokker-Planck equation stationary measure physical measure mesoscopic limit |
| DOI | 10.1007/s11425-019-1642-5 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied ; Mathematics |
| WOS ID | WOS:000558872800001 |
| Publisher | SCIENCE PRESS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51986 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Yi, Yingfei |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 4.Jilin Univ, Sch Math, Changchun 130012, Peoples R China |
| Recommended Citation 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. |
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