Skip to main content
Log in

Weak convergence of the extreme values of independent random variables in banach spaces with unconditional bases

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We generalize well-known results concerning the weak convergence of maxima of real independent random variables to the case of random variables taking values in the Banach spaces with unconditional bases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. B. V. Gnedenko, “Sur la distribution limit du terme maximum d’une serie aleatoire,” Ann. Math., 44, 423–453 (1943).

    Article  MathSciNet  Google Scholar 

  2. J. Galambos, The Asymptotic Theory of Extreme Order Statistics Wiley, New York-Chichester-Brisbane-Toronto (1978).

    MATH  Google Scholar 

  3. M. R. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer, New York-Heidelberg-Berlin 1986.

    Google Scholar 

  4. V. D. Mil’man, “Geometric theory of Banach spaces,” Usp. Mat. Nauk, 25, Issue 3, 113–174 (1970).

    MATH  MathSciNet  Google Scholar 

  5. J. Lindenstraus and L. Tzafriri, Classical Banach Spaces, Vol. 2, Springer, Berlin (1979).

    Google Scholar 

  6. I. K. Matsak and A. M. Plichko, On Maxima of Independent Random Variables in a Function Banach Lattice (to appear).

  7. I. K. Matsak, “Weak convergence of extreme values of independent Gaussian random variables in spaces l p , 1≤p<∞,” Teor. Ver. Mat. Statist. (to appear).

  8. N. N. Vakhaniya, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions in Banach Spaces [in Russian], Nauka, Moscow 1985.

    MATH  Google Scholar 

  9. J. Pickand, “Moment convergence of sample extremes,” Ann. Math. Statist., 39, No. 3, 881–889 (1968).

    Article  MathSciNet  Google Scholar 

  10. J.-P. Kahane, Some Random Series of Functions, Heath & Co (A Division of Raytheon Education Company), Lexington, Massachusetts (1968).

  11. S. A. Chobanyan and V. I. Tarieladze, “Gaussian characterizations of certain Banach spaces,” J. Multivar. Anal., 7, No. 1, 183–203 (1977).

    Article  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Matsak, I.K. Weak convergence of the extreme values of independent random variables in banach spaces with unconditional bases. Ukr Math J 48, 905–913 (1996). https://doi.org/10.1007/BF02384175

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384175

Keywords

Navigation