The Annals of Probability

Donsker's Invariance Principle for Lie Groups

Joseph C. Watkins

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Abstract

This paper establishes a functional central limit theorem for Lie groups under a mixing hypothesis. The main theorem generalizes results by Patrick Billingsley for Euclidean space and the author for the general linear group.

Article information

Source
Ann. Probab., Volume 17, Number 3 (1989), 1220-1242.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991265

Digital Object Identifier
doi:10.1214/aop/1176991265

Mathematical Reviews number (MathSciNet)
MR1009453

Zentralblatt MATH identifier
0688.60003

JSTOR
links.jstor.org

Subjects
Primary: 60B15: Probability measures on groups or semigroups, Fourier transforms, factorization
Secondary: 60F05: Central limit and other weak theorems 60F17: Functional limit theorems; invariance principles 60J30 60G10: Stationary processes

Keywords
Functional central limit theorem invariance principle in distribution Lie groups mixing martingale problem

Citation

Watkins, Joseph C. Donsker's Invariance Principle for Lie Groups. Ann. Probab. 17 (1989), no. 3, 1220--1242. doi:10.1214/aop/1176991265. https://projecteuclid.org/euclid.aop/1176991265


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