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Abstrakty
Some functional equations related to the notion of semistability of probability distributions on Z+ and R+ are studied. The solution sets of these equations are fully described.
Czasopismo
Rocznik
Tom
Strony
87--102
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- University of Indianapolis, Department of Mathematics and Computer Science, 1400 E. Hanna Ave., Indianapolis, IN 46227, USA
Bibliografia
- [1] R. J. Adler, R. E. Feldman and M. S. Taqqu (Eds.), A Practical Guide to Heavy Tailed Data, Birkhäuser, Boston, MA, 1998.
- [2] M. Ben Alaya and T. Huillet, On max-multiscaling distributions as extended maxsemistable ones, Stoch. Models 20 (2004), pp. 493-512.
- [3] M. Ben Alaya and T. Huillet, On a functional equation generalizing the class of semistable distributions, Ann. Inst. Statist. Math. 57 (2005), pp. 817-831.
- [4] M. Ben Alaya, T. Huillet and A. Porzio, On an extension of min-semistable distributions, Probab. Math. Statist. 27 (2007), pp. 303-323.
- [5] N. Bouzar, Discrete semi-stable distributions, Ann. Inst. Statist. Math. 56 (2004), pp. 497-510.
- [6] N. Bouzar, Semi-self-decomposable distributions on Z+, Ann. Inst. Statist. Math. 60 (2008), pp. 901-917.
- [7] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd edition, Wiley, New York 1968.
- [8] A. K. Gupta, K. Jagannathan, T. T. Nguyen and D. N. Shanbhag, Characterizations of stable laws via functional equations, Math. Nachr. 279 (2006), pp. 571-580.
- [9] K. van Harn and F. W. Steutel, Stability equations for processes with stationary independent increments using branching processes and Poisson mixtures, Stochastic Process. Appl. 45 (1993), pp. 209-230.
- [10] T. Huillet, A. Porzio and M. Ben Alaya, On Lévy stable and semistable distributions, Fractals 9 (2001), pp. 347-364.
- [11] S. Kotz, T. J. Kozubowski and K. Podgórski, The Laplace Distributions and Generalizations, Birkhäuser, Boston, MA, 2001.
- [12] P. Lévy, Théorie de l’addition des variables aléatoires, Gauthier-Villars, Paris 1937.
- [13] C. R. Rao and D. N. Shanbhag, Choquet-Deny Type Functional Equations with Applications to Stochastic Models, Wiley, Chichester 1994.
- [14] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, U.K., 1999.
- [15] F. W. Steutel and K. van Harn, Infinite Divisibility of Probability Distributions on the Real Line, Marcel Dekker, Inc., New York-Basel 2004.
Typ dokumentu
Bibliografia
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