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On the weak convergence of extremes in some Banach spaces
Author(s):
I.
K.
Matsak
Translated by:
V. Semenov
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika,
vipusk 69
(2003).
Journal:
Theor. Probability and Math. Statist.
No. 69
(2004),
141-152.
MSC (2000):
Primary 60B12
Posted:
February 9, 2005
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Additional information
Abstract:
The weak convergence of random elements
is studied for Banach spaces with an unconditional basis, where  and  ,  , are independent copies of a random element  .
References:
-
- 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 extreme 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 (1996), no. 6, 905-913 (1997). MR 1418157 (97i:60007)
- 5.
- -, On integral functionals of extreme value random functions, Teor. Imovir. Mat. Statist. 65 (2001), 110-120; English transl. in Theory Probab. Math. Statist. 65 (2001), 123-134. MR 1936135 (2004g:60010)
- 6.
- J. Lindenstraus and L. Tzafriri, Classical Banach Spaces, Springer-Verlag, Berlin, 1979. MR 0540367 (81c:46001)
- 7.
- J. Geffroy, Contributions à la théorie des valeurs extrêmes, Publ. Inst. Statist. Univ. Paris 7/8 (1958/59), 37-185. MR 0105168 (21:3911)
- 8.
- Ahmed E. Sarhan and Bernard G. Greenberg, Contributions to Order Statistics, Wiley, New York, 1962. MR 0169336 (29:6587)
- 9.
- E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin-Heidelberg-New York, 1976. MR 0453936 (56:12189)
- 10.
- J. Galambos and E. Seneta, Regularly varying sequences, Proc. Amer. Math. Soc. 41 (1973), 110-116. MR 0323963 (48:2316)
- 11.
- N. N. Vakhania, V. I. Tarieladze, and S. A. Chobanyan, Probability Distributions on Banach Spaces, ``Nauka'', Moscow, 1985; English transl., Kluwer, Dordrecht, 1987. MR 0787803 (86j:60014)
- 12.
- I. K. Matsak and A. M. Plichko, On maxima of independent random elements in a Banach function lattice, Teor. Imovir. Matem. Statist. 61 (1999), 105-116; English transl. in Theory Probab. Math. Statist. 61 (2000), 109-120. MR 1866964 (2002k:60020)
- 13.
- J. Pickands, Moment convergence of sample extremes, Ann. Math. Statist. 39 (1968), 881-889. MR 0224231 (36:7275)
- 14.
- S. A. Chobanyan and V. I. Tarieladze, Gaussian characterizations of certain Banach spaces, J. Multivar. Anal. 7 (1977), no. 1, 183-203. MR 0433572 (55:6545)
- 15.
- J.-P. Kahane, Some Random Series of Functions, D. C. Heath, Lexington, MA, 1968. MR 0254888 (40:8095)
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Additional Information:
I.
K.
Matsak
Affiliation:
Kyiv National University of Technology and Design, Nemyrovych-Danchenko Street 2, Kyiv 02011, Ukraine
Email:
infor1@vtv.kiev.ua
DOI:
10.1090/S0094-9000-05-00621-6
PII:
S 0094-9000(05)00621-6
Received by editor(s):
26/JUN/2002
Posted:
February 9, 2005
Copyright of article:
Copyright
2005,
American Mathematical Society
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