A nonlinear deformation of Wiener space

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	A nonlinear deformation of Wiener space
	Luo, SL
	1998-04-01
发表期刊	JOURNAL OF THEORETICAL PROBABILITY
ISSN	0894-9840
卷号	11 期号:2 页码:331-350
摘要	Based on the complex hyperbolic geometry associated with discrete series of SU(1, 1), we construct a quasi-invariant and ergodic measure on infinite product of Poincare disc and a hyperbolic analogue of numerical Wiener space which turns out to be a nonlinear deformation of the Wiener space. An integration by parts formula is established. We also investigate the orthogonal decomposition of the L-2-holomorphic functions which is an analogue of the Wiener-Ito-Segal decomposition. In the zero-curvature and large spin limit, we recover the linear Wiener space.
关键词	Wiener space Poincare disc Bergman measure quasi invariance ergodicity integration by parts orthogonal decomposition
语种	英语
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000073666000002
出版者	PLENUM PUBL CORP
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/13833
专题	应用数学研究所
通讯作者	Luo, SL
作者单位	Acad Sinica, Inst Appl Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Luo, SL. A nonlinear deformation of Wiener space[J]. JOURNAL OF THEORETICAL PROBABILITY,1998,11(2):331-350.
APA	Luo, SL.(1998).A nonlinear deformation of Wiener space.JOURNAL OF THEORETICAL PROBABILITY,11(2),331-350.
MLA	Luo, SL."A nonlinear deformation of Wiener space".JOURNAL OF THEORETICAL PROBABILITY 11.2(1998):331-350.