Singular HJB equations with applications to KPZ on the real line

doi:10.1007/s00440-022-01137-w

	Singular HJB equations with applications to KPZ on the real line
	Zhang, Xicheng 1,2; Zhu, Rongchan 2; Zhu, Xiangchan 3
刊名	PROBABILITY THEORY AND RELATED FIELDS
	2022-05-13
页码	81
关键词	Singular SPDEs HJB equations KPZ equations Paracontrolled distributions Global well-posedness Zvonkin's transformation
ISSN号	0178-8051
DOI	10.1007/s00440-022-01137-w
英文摘要	This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which are not well-defined in the classical sense and are understood by using the paracontrolled distribution method introduced in (Gubinelli et al. in Forum Math Pi 3(6):1, 2015). By a new characterization of weighted Holder spaces and Zvonkin's transformation we prove some new a priori estimates, and therefore establish the global well-posedness for singular HJB equations. As applications, we obtain global well-posedness in polynomial weighted Holder spaces for KPZ type equations on the real line, as well as modified KPZ equations for which the Cole-Hopf transformation is not applicable.
资助项目	National Key R&D Program of China[2020YFA0712700] ; NSFC[11731009] ; NSFC[12131019] ; NSFC[11922103] ; NSFC[12090014] ; NSFC[11688101] ; key Lab of Random Complex Structures and Data Science, Youth Innovation Promotion Association, Chinese Academy of Science[2020003] ; DFG[CRC 1283]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000795193800002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/61348]
专题	中国科学院数学与系统科学研究院
通讯作者	Zhu, Rongchan
作者单位	1.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 2.Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Xicheng,Zhu, Rongchan,Zhu, Xiangchan. Singular HJB equations with applications to KPZ on the real line[J]. PROBABILITY THEORY AND RELATED FIELDS,2022:81.
APA	Zhang, Xicheng,Zhu, Rongchan,&Zhu, Xiangchan.(2022).Singular HJB equations with applications to KPZ on the real line.PROBABILITY THEORY AND RELATED FIELDS,81.
MLA	Zhang, Xicheng,et al."Singular HJB equations with applications to KPZ on the real line".PROBABILITY THEORY AND RELATED FIELDS (2022):81.