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Theory of Probability and Mathematical Statistics

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The asymptotic stability of the maximum of independent random elements in function Banach lattices


Authors: K. S. Akbash and I. K. Matsak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 1-11
MSC (2010): Primary 60B12
DOI: https://doi.org/10.1090/S0094-9000-2013-00885-0
Published electronically: August 20, 2013
MathSciNet review: 2986446
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Abstract: We generalize some well-known results on the asymptotic stability of the maximum of independent random variables in $ \mathbb{R}^1 $ to the case of $ q$-concave Banach ideal spaces. A theorem on the relative asymptotic stability of the maximum of independent random elements in function Banach lattices is proved.


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Additional Information

K. S. Akbash
Affiliation: Operations Research Department, Faculty for Cybernetics, Kiev National Taras Shevchenko University, Glushkov Avenue 2, Building 6, Kyiv 03127, Ukraine
Email: k{\textunderscore}m{\textunderscore}s{\textunderscore}kirovograd@mail.ru

I. K. Matsak
Affiliation: Operations Research Department, Faculty for Cybernetics, Kiev National Taras Shevchenko University, Glushkov Avenue 2, Building 6, Kyiv 03127, Ukraine
Email: ivanmatsak@gmail.com

DOI: https://doi.org/10.1090/S0094-9000-2013-00885-0
Keywords: Maximum of independent random elements, asymptotic stability, Banach ideal spaces
Received by editor(s): May 19, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society