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http://dx.doi.org/10.4134/JKMS.j160361

REGULAR VARIATION AND STABILITY OF RANDOM MEASURES  

Quang, Nam Bui (Academy of Air Defence and Air Forces)
Dang, Phuc Ho (Institute of Mathematics Vietnam Academy of Sciences and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.3, 2017 , pp. 1049-1061 More about this Journal
Abstract
The paper presents a characterization of stable random measures, giving a canonical form of their Laplace transform. Domain of attraction of stable random measures is concerned in a theorem showing that a random measure belongs to domain of attraction of any stable random measures if and only if it varies regularly at infinity.
Keywords
random measure; stable; domain of attraction; regular variation;
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1 H. Hult and F. Lindskog, Regular variation for measures on metric spaces, Publ. Inst. Math. 80(94) (2006), 121-140.   DOI
2 R. Jajte, On stable distributions in Hilbert space, Studia Math. 30 (1968), 63-71.   DOI
3 O. Kallenberg, Random Measures, 3rd Edition, Akademie-Verlag, Berlin, 1983.
4 A. Kumar and V. Mandrenkar, Stable probability measures on Banach spaces, Studia Math. 42 (1972), 133-144.   DOI
5 P. Levy, Theorie de l'addition des variables aleatoires, Gauthier-Villars, Paris, 1937.
6 J. McCulloch, Financial applications of stable distributions, Handbook of Statistics 14, 393-425, ed. G. Maddala and C. Rao, Elsevier Science Publishers, North-Holland, 1996.
7 Thu Nguyen Van, Stable random measures, Acta Math. Vietnam. 4 (1979), no. 1, 71-75.
8 K. J. Palmer, M. S. Ridout, and B. J. T. Morgan, Modelling cell generation times using the tempered stable distribution, J. Roy. Statist. Soc. Ser. C 57 (2008), no. 4, 379-397.   DOI
9 S. I. Resnik, Heavy-Tail Phenomena: Probabilistic and Statistical Modeling, Springer, New York 2007.
10 G. Samorodnitsky and M. S. Taqqu, Stable non-Gaussian random processes, Chapman and Hall, London 1994.
11 K. Sato, Strictly operator-stable distributions, J. Multivariate Anal. 22 (1987), no. 2, 278-295.   DOI
12 V. M. Zolotarev, One-dimensional stable distributions, Translations of Mathematical Monographs, 65. American Mathematical Society, 1986.
13 R. J. Adler, R. E. Feldman, and M. S. Taqqu, A Practical Guide to Heavy Tailed Data, Birkhauser, Boston, 1998.
14 Y. Davydov, I. Molchanov, and S. Zuyev, Strictly stable distributions on convex cones, Electron. J. Probab. 13 (2008), no. 11, 259-321.   DOI
15 Y. Davydov, I. Molchanov, and S. Zuyev, Stability for random measures, point processes and discrete semigroups, Bernoulli 17 (2011), no. 3, 1015-1043.   DOI
16 J. L. Geluk and L. de Haan, Stable probability distributions and their domains of attraction: A direct approach, Probab. Math. Statist. 20 (2000), no. 1, 169-188.
17 B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sum of Independent Random Variables Addison-Wesley, 1954.