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A counting process in the max-scheme


Author: I. K. Matsak
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
Journal: Theor. Probability and Math. Statist. 91 (2015), 115-129
MSC (2010): Primary 60G70
DOI: https://doi.org/10.1090/tpms/971
Published electronically: February 4, 2016
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Abstract | References | Similar Articles | Additional Information

Abstract: The exact asymptotic behavior of a counting process is studied for the max-scheme in the case of independent random variables.


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

  • 1. V. V. Buldygin, K.-H. Indlekofer, O. I. Klesov, and J. G. Steinebach, Pseudo-Regularly Varying Functions and Generalized Renewal Processes, `TViMS'', Kyiv, 2012. (Ukrainian)
  • 2. J. Galambos, The Asymptotic Theory of Extreme Order Statistics, John Wiley & Sons, New York, 1978. MR 489334 (80b:60040)
  • 3. Ole Barndorff-Nielsen, On the limit behaviour of extreme order statistics, Ann. Math. Statist. 34 (1963), no. 3, 992-1002. MR 0150889 (27:875)
  • 4. J. Pickands, An iterated logarithm law for the maximum in a stationary Gaussian sequence, Z. Warhscheinlichkeitstheorie verw. Geb. 12 (1969), no. 3, 344-355. MR 0251776 (40:5003)
  • 5. L. de Haan and A. Hordijk, The rate of growth of sample maxima, Ann. Math. Statist. 43 (1972), 1185-1196. MR 0312550 (47:1107)
  • 6. M. J. Klass, The Robbins-Siegmund criterion for partial maxima, Ann. Probab. 13 (1985), 1369-1370. MR 806233 (87b:60046)
  • 7. L.  de Haan and A. Ferreira, Extreme Values Theory: An Introduction, Springer, Berlin, 2006. MR 2234156 (2007g:62008)
  • 8. K. S. Akbash and I. K. Matsak, An improvement of the law of the iterated logarithm for the max-scheme, Ukr. Mat. Zh. 64 (2012), no. 8, 1132-1137; English transl in Ukrainian Math. J. 64 (2013), no. 8, 1290-1296. MR 3104866
  • 9. I. K. Matsak, Asymptotic behavior of a counting process in the max-scheme, Ukr. Mat. Zh. 65 (2013), no. 11, 1575-1579; English transl in Ukrainian Math. J. 65 (2014), no. 11, 1743-1748. MR 3216868
  • 10. I. Matsak and I. Rozora, Asymptotic behaviour of counting process in the max-scheme. Discrete case, Georg. Math. J. (to appear)
  • 11. G. M. Fikhtengol'ts, Course of Differential and Integral Calculus, vol. 2, ``Nauka'', Moscow, 1969. (Russian)
  • 12. M. R. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer-Verlag, New York, Heidelberg, Berlin, 1983. MR 691492 (84h:60050)
  • 13. E. Seneta, Regularly Varying Functions, Springer-Verlag, New York-Heidelberg-Berlin, 1976. MR 0453936 (56:12189)
  • 14. G. Pólya and G. Szegö, Problems and Theorems in Analysis I: Series, Integral Calculus, Theory of Functions, Springer-Verlag, New York-Heidelberg-Berlin, 1972. MR 0344042 (49:8782)

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Additional Information

I. K. Matsak
Affiliation: Faculty for Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: ivanmatsak@univ.kiev.ua

DOI: https://doi.org/10.1090/tpms/971
Keywords: Maximum of independent random variables, counting process, almost sure behavior
Received by editor(s): August 6, 2014
Published electronically: February 4, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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