Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 
 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. O. Barndorff-Nielsen, On the limit behaviour of extreme order statistics, Ann. Math. Statist. 34 (1963), no. 3, 992-1002. MR 0150889 (27:875)
  • 2. W. Feller, An Introduction to Probability Theory and Its Applications, vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1971. MR 0270403 (42:5292)
  • 3. J. Galambos, The Asymptotic Theory of Extreme Order Statistics, John Wiley & Sons, New York-Chichester-Brisbane, 1978. MR 489334 (80b:60040)
  • 4. B. V. Gnedenko, Sur la distribution limit du terme maximum d'une serie aleatoire, Ann. Math. 44 (1943), no. 3, 423-453. MR 0008655 (5:41b)
  • 5. L. V. Kantorovich and G. P. Akilov, Functional Analysis, ``Nauka'', Moscow, 1984; English transl., Pergamon Press, Oxford-Elmsford, N.Y., 1982. MR 664597 (83h:46002)
  • 6. J. Lindenstraus and L. Tzafriri, Classical Banach Spaces, Springer-Verlag, Berlin-New York, 1973. MR 0415253 (54:3344)
  • 7. I. K. Matsak, Estimates for the moments of the supremum of normalized sums of independent random variables, Teor. Imovirnost. Matem. Statist. 67 (2002), 104-116; English transl. in Theory Probab. Mathem. Statist. 67 (2003), 115-128. MR 1956624 (2004i:60061)
  • 8. I. K. Matsak and A. M. Plichko, On the maxima of independent random elements in a Banach functional lattice, Teor. Imovir. Mat. Stat. 61 (1999), 105-116; English transl. in Theory Probab. Math. Statist. 61 (2000), 109-120. MR 1866964 (2002k:60020)
  • 9. J. Pickands, Moment convergence of sample extremes, Ann. Math. Statist. 39 (1968), no. 3, 881-889. MR 0224231 (36:7275)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60B12

Retrieve articles in all journals with MSC (2010): 60B12


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

American Mathematical Society