NOISE-VANISHING CONCENTRATION AND LIMIT BEHAVIORS OF PERIODIC PROBABILITY SOLUTIONS

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	NOISE-VANISHING CONCENTRATION AND LIMIT BEHAVIORS OF PERIODIC PROBABILITY SOLUTIONS
	Ji, Min 1,3; Qi, Weiwei 2,3,4; Shen, Zhongwei 2; Yi, Yingfei 2,5
	2020-05-01
发表期刊	DIFFERENTIAL AND INTEGRAL EQUATIONS
ISSN	0893-4983
卷号	33 期号:5-6 页码:273-322
摘要	The present paper is devoted to the investigation of noisy impacts on the dynamics of periodic ordinary differential equations (ODEs). To do so, we consider a family of stochastic differential equations resulting from a periodic ODE perturbed by small white noises, and study noise-vanishing behaviors of their "steady states" that are characterized by periodic probability solutions of the associated Fokker-Plank equations. By establishing noise-vanishing concentration estimates of periodic probability solutions, we prove that any limit measure of periodic probability solutions must be a periodically invariant measure of the ODE and that the global periodic attractor of a dissipative ODE is stable under general small noise perturbations. For local periodic attractors (resp. local periodic repellers), small noises are constructed to stabilize (resp. de-stabilize) them. Our study provides an elementary step towards the understanding of stochastic stability of periodic ODEs.
收录类别	SCI
语种	英语
资助项目	NSFC[11571344] ; China Scholarship Council ; University of Alberta ; NSERC[RGPIN-2018-04371] ; NSERC[DGECR-2018-00353] ; NSERC[1257749] ; PIMS CRG grant ; Jilin University
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000548743700005
出版者	KHAYYAM PUBL CO INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51814
专题	中国科学院数学与系统科学研究院
通讯作者	Ji, Min
作者单位	1.Acad Math & Syst Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Jilin Univ, Sch Math, Changchun 130012, Peoples R China
推荐引用方式 GB/T 7714	Ji, Min,Qi, Weiwei,Shen, Zhongwei,et al. NOISE-VANISHING CONCENTRATION AND LIMIT BEHAVIORS OF PERIODIC PROBABILITY SOLUTIONS[J]. DIFFERENTIAL AND INTEGRAL EQUATIONS,2020,33(5-6):273-322.
APA	Ji, Min,Qi, Weiwei,Shen, Zhongwei,&Yi, Yingfei.(2020).NOISE-VANISHING CONCENTRATION AND LIMIT BEHAVIORS OF PERIODIC PROBABILITY SOLUTIONS.DIFFERENTIAL AND INTEGRAL EQUATIONS,33(5-6),273-322.
MLA	Ji, Min,et al."NOISE-VANISHING CONCENTRATION AND LIMIT BEHAVIORS OF PERIODIC PROBABILITY SOLUTIONS".DIFFERENTIAL AND INTEGRAL EQUATIONS 33.5-6(2020):273-322.