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
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
Full-text PDF Free Access
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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.
References
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References
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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_m_s_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
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
