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The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients
Luo, Dejun1,2
2018
Source PublicationSTOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
ISSN1744-2508
Volume90Issue:3Pages:379-410
AbstractWe study the degenerate Ito SDE on R-d whose drift coefficient only fulfills a mixed Osgood and Sobolev regularity. Under suitable assumptions on the gradient of the diffusion coefficient and on the divergence of the drift coefficient, we prove the existence and uniqueness of generalized stochastic flows associated to such equations. We also prove the uniqueness of solutions to the corresponding Fokker-Planck equation by using the probabilistic method.
KeywordStochastic differential equation Osgood and Sobolev condition DiPerna-Lions theory Fokker-Planck equation stochastic flow
DOI10.1080/17442508.2017.1357723
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Statistics & Probability
WOS IDWOS:000427283600004
PublisherTAYLOR & FRANCIS LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29911
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Random Complex Struct & Data Sci, Beijing, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
Recommended Citation
GB/T 7714
Luo, Dejun. The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES,2018,90(3):379-410.
APA Luo, Dejun.(2018).The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients.STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES,90(3),379-410.
MLA Luo, Dejun."The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients".STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES 90.3(2018):379-410.
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