Quantitative concentration of stationary measures

doi:10.1016/j.physd.2019.04.006

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	Quantitative concentration of stationary measures
	Ji, Min1,2 ; Shen, Zhongwei 3; Yi, Yingfei 3,4
	2019-12-01
发表期刊	PHYSICA D-NONLINEAR PHENOMENA
ISSN	0167-2789
卷号	399 页码:73-85
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.
关键词	Fokker-Planck equation Stationary measure Qualitative concentration Stochastic stability Lyapunov function
DOI	10.1016/j.physd.2019.04.006
语种	英语
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
WOS类目	Mathematics, Applied ; Physics, Fluids & Plasmas ; Physics, Multidisciplinary ; Physics, Mathematical
WOS记录号	WOS:000482872900006
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/35640
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.Univ Chinese Acad Sci, Chinese Acad Sci, Beijing 100080, Peoples R China 3.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 4.Jilin Univ, Sch Math, Changchun 130012, Jilin, 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.