Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient

doi:10.1016/j.bulsci.2009.01.002

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	Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient
	Luo, Dejun
	2009-04-01
发表期刊	BULLETIN DES SCIENCES MATHEMATIQUES
ISSN	0007-4497
卷号	133 期号:3 页码:205-228
摘要	We consider the stochastic flow generated by Stratonovich stochastic differential equations with non-Lipschitz drift coefficients. Based on the author's previous works, we show that if the generalized divergence of the drift is bounded, then the Lebesgue measure on R(d) is quasi-invariant under the action of the stochastic flow, and the explicit expression of the Radon-Nikodym derivative is also presented. Finally we show in a special case that the unique solution of the corresponding Fokker-Planck equation is given by the density of the stochastic flow. (C) 2009 Elsevier Masson SAS. All rights reserved.
关键词	Stochastic flow Stochastic differential equation Quasi-invariance of measure Non-Lipschitz condition Fokker-Planck equation
DOI	10.1016/j.bulsci.2009.01.002
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000265475000001
出版者	GAUTHIER-VILLARS/EDITIONS 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/8903
专题	应用数学研究所
通讯作者	Luo, Dejun
作者单位	Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Luo, Dejun. Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient[J]. BULLETIN DES SCIENCES MATHEMATIQUES,2009,133(3):205-228.
APA	Luo, Dejun.(2009).Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient.BULLETIN DES SCIENCES MATHEMATIQUES,133(3),205-228.
MLA	Luo, Dejun."Quasi-invariance of Lebesgue measure under the homeomorphic flow generated by SDE with non-Lipschitz coefficient".BULLETIN DES SCIENCES MATHEMATIQUES 133.3(2009):205-228.