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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

On the weak convergence of extremes in some Banach spaces


Author: I. K. Matsak
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 69 (2003).
Journal: Theor. Probability and Math. Statist. 69 (2004), 141-152
MSC (2000): Primary 60B12
Published electronically: February 9, 2005
MathSciNet review: 2110912
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Abstract | References | Similar Articles | Additional Information

Abstract: The weak convergence of random elements

\begin{displaymath}U_n=b_n (Z_n -a_n \mathfrak{S}) \end{displaymath}

is studied for Banach spaces with an unconditional basis, where $Z_n= \max _{1\leq k \leq n} X_k$ and $X_k$, $k\geq 1$, are independent copies of a random element $X$.


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Additional Information

I. K. Matsak
Affiliation: Kyiv National University of Technology and Design, Nemyrovych-Danchenko Street 2, Kyiv 02011, Ukraine
Email: infor1@vtv.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00621-6
PII: S 0094-9000(05)00621-6
Received by editor(s): June 26, 2002
Published electronically: February 9, 2005
Article copyright: © Copyright 2005 American Mathematical Society