The Annals of Probability

An Extended Martingale Invariance Principle

D. L. McLeish

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Abstract

In this note the conditions on an invariance principle for triangular arrays of random variables contained in an earlier paper are weakened. Random norming by functions which are not stopping times is permitted, the $L^2$-boundedness conditions on the maximum of the summands relaxed, and joint convergence with an arbitrary sequence of random elements of some other metric space proved.

Article information

Source
Ann. Probab., Volume 6, Number 1 (1978), 144-150.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995619

Digital Object Identifier
doi:10.1214/aop/1176995619

Mathematical Reviews number (MathSciNet)
MR471032

Zentralblatt MATH identifier
0379.60046

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G45

Keywords
Invariance principle Donsker's theorem central limit theorem martingales

Citation

McLeish, D. L. An Extended Martingale Invariance Principle. Ann. Probab. 6 (1978), no. 1, 144--150. doi:10.1214/aop/1176995619. https://projecteuclid.org/euclid.aop/1176995619


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