THE WIENER SPHERE AND WIENER MEASURE
成果类型：
Article
署名作者：
CUTLAND, N; NG, SA
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989390
发表日期：
1993
页码：
1-13
关键词：
摘要：
The Loeb measure construction of nonstandard analysis is used to define uniform probability mu(L) on the infinite-dimensional sphere of Poincare, Wiener and Levy, and we construct Wiener measure from it, thus giving rigorous sense to the informal discussion by McKean. From this follows an elementary proof of a weak convergence result. The relation to the infinite product of Gaussian measures is studied. We investigate transformations of the sphere induced by shifts and the associated transformations of mu(L). The Cameron-Martin density is derived as a Jacobian. We also prove a dichotomy theorem for the family of shifted measures.
来源URL：