Towards mesoscopic ergodic theory

doi:10.1007/s11425-019-1642-5

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	Towards mesoscopic ergodic theory
	Qi, Weiwei 1,2,3; Shen, Zhongwei 3; Wang, Shirou 3; Yi, Yingfei 3,4
	2020-08-10
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	24
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.
关键词	ergodic theory stochastic differential equation Fokker-Planck equation stationary measure physical measure mesoscopic limit
DOI	10.1007/s11425-019-1642-5
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000558872800001
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51986
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.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
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.