The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients

doi:10.1080/17442508.2017.1357723

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	The Ito SDEs and Fokker-Planck equations with Osgood and Sobolev coefficients
	Luo, Dejun1,2
刊名	STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
	2018
卷号	90 期号:3 页码:379-410
关键词	Stochastic differential equation Osgood and Sobolev condition DiPerna-Lions theory Fokker-Planck equation stochastic flow
ISSN号	1744-2508
DOI	10.1080/17442508.2017.1357723
英文摘要	We 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.
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000427283600004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/29910]
专题	应用数学研究所
通讯作者	Luo, Dejun
作者单位	1.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
推荐引用方式 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.