Wick calculus for nonlinear Gaussian functionals

doi:10.1007/s10255-008-8808-0

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	Wick calculus for nonlinear Gaussian functionals
	Hu, Yao-zhong 1; Yan, Jia-an2
	2009-07-01
发表期刊	ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES
ISSN	0168-9673
卷号	25 期号:3 页码:399-414
摘要	This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random variables. Some conditions are described for random variables whose Wick product or whose renormalization are integrable random variables. Relevant results on multiple Wiener integrals, second quantization operator, Malliavin calculus and their relations with the Wick product and Wick renormalization are also briefly presented. A useful tool for Wick product is the S-transform which is also described without the introduction of generalized random variables.
关键词	Malliavin calculus multiple integral chaos decomposition Wick product Wick renormalization
DOI	10.1007/s10255-008-8808-0
语种	英语
资助项目	National Science Foundation[DMS0504783] ; International Research Team on Complex Systems, Chines Academy of Sciences ; National Natural Science Foundation of China[10571167] ; National Basic Research Program of China[2007CB814902] ; Science Fund for Creative Research Groups[10721101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000266479900005
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8036
专题	应用数学研究所
通讯作者	Hu, Yao-zhong
作者单位	1.Univ Kansas, Dept Math, Lawrence, KS 66045 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Hu, Yao-zhong,Yan, Jia-an. Wick calculus for nonlinear Gaussian functionals[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,2009,25(3):399-414.
APA	Hu, Yao-zhong,&Yan, Jia-an.(2009).Wick calculus for nonlinear Gaussian functionals.ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES,25(3),399-414.
MLA	Hu, Yao-zhong,et al."Wick calculus for nonlinear Gaussian functionals".ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 25.3(2009):399-414.