Open Access
August, 1985 A Note on a Limit Theorem for Differentiable Mappings
K. A. Borovkov
Ann. Probab. 13(3): 1018-1021 (August, 1985). DOI: 10.1214/aop/1176992924


The main purpose of this paper is to draw attention to a simple and useful general "continuity theorem" type result, from which a great deal of limit theorems follow as almost immediate consequences. As an example, we give a new very short and transparent proof of the recent result by H. Teicher and C. Hagwood (A multidimensional CLT for maxima of normed sums); in fact, a much more general assertion is proved here. Another application of the main result establishes a correspondence between the convergence of empirical and quantile processes. (A similar result holds for the renewal and partial sums processes.)


Download Citation

K. A. Borovkov. "A Note on a Limit Theorem for Differentiable Mappings." Ann. Probab. 13 (3) 1018 - 1021, August, 1985.


Published: August, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0574.60047
MathSciNet: MR799438
Digital Object Identifier: 10.1214/aop/1176992924

Primary: 60F17
Secondary: 60F05

Keywords: Weak convergence and mappings , Weak invariance principle

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 3 • August, 1985
Back to Top