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Tytuł artykułu

Stable probability distributions and their domains of attraction : a direct approach

Wybrane pełne teksty z tego czasopisma
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.
Rocznik
Strony
169--188
Opis fizyczny
Bibliogr.19 poz.
Twórcy
autor
  • Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738 , NL-3000 DR Rotterdam, The Netherlands
autor
  • Econometric Institute, Erasmus University Rotterdam, P.O. Box 1738 , NL-3000 DR Rotterdam, The Netherlands
Bibliografia
  • [1] N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation, Encyclopedia Math. Appl. 27, Cambridge Univ. Press, 1987.
  • [2] L. Вreiman, Probability, Addison-Wesley, Reading MA, 1968.
  • [3] Y. S. Chow and H. Teicher, Probability Theory, Independence, Interchangeability, Martingales, Springer, Berlin 1978.
  • [4] R. M. Dudley, Real Analysis and Probability, Wadsworth and Brooks/Cole, 1989.
  • [5] E. Fama, The behavior of stock prices, Journal of Business 38 (1965), pp.34-105.
  • [6] W. Feller, An Introduction to Probability Theory and Its Applications 2,2nd ed., Wiley, New York 1971.
  • [7] J. L. Geluk and L. de Haan, Regular Variation, Extensions and Tauberian Theorems, CWI Tract 40, Amsterdam 1987.
  • [8] В. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading MA, 1954.
  • [9] E. Hewitt and K. Stromberg, Real and Abstract Analysis, Springer, Berlin 1969.
  • [10] I. A. Ibragimov and Yu. V. Linnik, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen 1971.
  • [11] D. G. Kendall, Delphic semigroups, infinitely divisible regenerative phenomena and the arithmetic of p-functions, Z. Wahrsch. verw. Gebiete 9 (1968), pp. 163-195.
  • [12] R. M. Kunst, Apparently stable increments in finance data: Could ARCH effects be the cause?, J. Statist. Comput. Simulation 45 (1993), pp. 121-127.
  • [13] P. Levy, Theorie de Vaddition des variables aléatoires, 2nd ed., Gauthier Villars, Paris 1954.
  • [14] B. Mandelbrot, The variation of certain speculative prices, Journal of Business 36 (1963), pp. 394-419.
  • [15] E. J. G. Pitman, On the behaviour of the characteristic function of a probability distribution in the neighbourhood of the origin, J. Austral. Math. Soc. Ser. A 29 (1968), pp. 337-347.
  • [16] G. Samorodnitsky and M. S. Taqqu, Stable non-Gaussian random processes, Chapman and Hall, London 1994.
  • [17] P. Samuelson, Efficient portfolio selection for Pareto-Lévy investments, Journal of Financial and Quantitative Analysis 2 (1967), pp. 107-117.
  • [18] F. W. Steutel, Problem 979, Problem Section, Nieuw. Arch. Wisk. 15 (3), p. 252.
  • [19] V. M. Zolotarev, One-dimensional stable distributions, Transí. Math. Monographs, Vol. 65, American Mathematical Society, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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