| Existence of periodic probability solutions to Fokker-Planck equations with applications | |
Ji, Min1,2,3 ; Qi, Weiwei3,4; Shen, Zhongwei4; Yi, Yingfei4,5
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| 2019-12-01 | |
| Source Publication | JOURNAL OF FUNCTIONAL ANALYSIS
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| ISSN | 0022-1236 |
| Volume | 277Issue:11Pages:41 |
| Abstract | In the present paper, we consider a Fokker-Planck equation associated to periodic stochastic differential equations with irregular coefficients. We define periodic probability solutions to be periodic analogs of stationary measures for stationary Fokker-Planck equations, and study their existence in both non-degenerate and degenerate cases. In the non-degenerate case, a Lyapunov condition is imposed to ensure the existence of periodic probability solutions to the Fokker-Planck equation with Sobolev coefficients. In the degenerate case with slightly more regular coefficients, the existence is established under the same Lyapunov condition. As applications of our results, we construct periodic probability solutions to Fokker-Planck equations associated to stochastic damping Hamiltonian systems and stochastic differential inclusions. (C) 2019 Elsevier Inc. All rights reserved. |
| Keyword | Fokker-Planck equation Periodic probability solution Stochastic differential inclusion Stochastic damping Hamiltonian system |
| DOI | 10.1016/j.jfa.2019.108281 |
| Language | 英语 |
| Funding Project | NSFC[10421101] ; NSFC[11571344] ; China Scholarship Council ; University of Alberta ; NSERC[RGPIN-2018-04371] ; NSERC[DGECR-2018-00353] ; NSERC[1257749] ; PIMS CRG grant ; Jilin University |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics |
| WOS ID | WOS:000489357700009 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/35796 |
| Collection | 数学所 |
| Corresponding Author | Qi, Weiwei |
| Affiliation | 1.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 4.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada 5.Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China |
| Recommended Citation GB/T 7714 | Ji, Min,Qi, Weiwei,Shen, Zhongwei,et al. Existence of periodic probability solutions to Fokker-Planck equations with applications[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2019,277(11):41. |
| APA | Ji, Min,Qi, Weiwei,Shen, Zhongwei,&Yi, Yingfei.(2019).Existence of periodic probability solutions to Fokker-Planck equations with applications.JOURNAL OF FUNCTIONAL ANALYSIS,277(11),41. |
| MLA | Ji, Min,et al."Existence of periodic probability solutions to Fokker-Planck equations with applications".JOURNAL OF FUNCTIONAL ANALYSIS 277.11(2019):41. |
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