Two hyperfinite constructions of the brownian bridge
作者:
GonzaloR. Mendieta,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1989)
卷期:
Volume 7,
issue 1
页码: 75-88
ISSN:0736-2994
年代: 1989
DOI:10.1080/07362998908809168
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process
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