Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

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

 
 

 

Limit distributions of extreme values of bounded independent random functions


Author: I. K. Matsak
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 129-138
MSC (2000): Primary 60B12, 60G70
DOI: https://doi.org/10.1090/S0094-9000-05-00653-8
Published electronically: December 28, 2005
MathSciNet review: 2144326
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the limit probabilities that extreme values of a sequence of independent normal random functions belong to extending intervals.


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

  • 1. B. V. Gnedenko, Sur la distribution limit du terme maximum d'une série aléatoire, Ann. Math. 44 (1943), 423-453. MR 0008655 (5:41b)
  • 2. J. Galambos, The Asymptotic Theory of Extreme Order Statistics, Wiley, New York-Chichester-Brisbane-Toronto, 1978. MR 0489334 (80b:60040)
  • 3. M. R. Leadbetter, G. Lindgren, and H. Rootzén, Extremes and Related Properties of Random Sequences and Processes, Springer, New York, 1983. MR 0691492 (84h:60050)
  • 4. I. K. Matsak, The weak convergence of extremal values of independent random elements in Banach spaces with an unconditional basis, Ukr. Matem. Zh. 48 (1996), no. 6, 805-812; English transl. in Ukrain. Math. J. 48 (1997), no. 6, 905-913. MR 1418157 (97i:60007)
  • 5. I. K. Matsak, On integral functionals of extreme value random functions, Teor. Imovir. ta Matem. Statist. 65 (2001), 110-120; English transl. in Theor. Probability and Math. Statist. 65 (2002), 123-134. MR 1936135 (2004g:60010)
  • 6. B. M. Brown and S. I. Resnick, Extreme values of independent stochastic processes, J. Appl. Probab. 14 (1977), 732-739. MR 0517438 (58:24470)
  • 7. I. K. Matsak, Asymptotic properties of the norm of the extremal value in the sequence of normal random functions, Ukr. Matem. Zh. 50 (1998), no. 10, 1359-1365; English transl. in Ukrain. Math. J. 50 (1999), no. 10, 1405-1415. MR 1711233 (2000g:60064)
  • 8. A. V. Bukhvalov, A. I. Veksler, and V. A. Geiler, Normed lattices, Itogi Nauki i Tekhniki, Mathematical Analysis, vol. 18, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1980, pp. 125-184. MR 0597904 (82b:46019)
  • 9. J. Lindenstraus and L. Tzafriri, Classical Banach Spaces, vol. 2, Springer, Berlin, 1979. MR 0540367 (81c:46001)
  • 10. M. A. Lifshits, Gaussian Random Functions, TViMS, Kiev, 1995; English transl., Kluwer, Dordrecht, 1995. MR 1472736 (98k:60059)
  • 11. H. Cramér and M. R. Leadbetter, Stationary and Related Stochastic Processes, Wiley, New York, 1967. MR 0217860 (36:949)
  • 12. Yu. K. Belyaev and V. I. Piterbarg, Asymptotic behavior of the mean value of $ A$-points of outliers of a Gaussian field for a high level, Dokl. Akad. Nauk SSSR, 203 (1972), no. 1, 9-12. (Russian) MR 0300334 (45:9380)
  • 13. C. Qualls and H. Watanabe, Asymptotic properties of Gaussian processes, Ann. Math. Statist. 43 (1972), 580-596. MR 0307318 (46:6438)

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60B12, 60G70

Retrieve articles in all journals with MSC (2000): 60B12, 60G70


Additional Information

I. K. Matsak
Affiliation: Kyiv National University for Design and Technology, Nemyrovych-Danchenko Street 2, 01601, Kyiv–11, Ukraine
Email: infor1@vtv.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-05-00653-8
Received by editor(s): January 13, 2002
Published electronically: December 28, 2005
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society