본문 바로가기
KERD
논문KCI 등재

REGULAR VARIATION AND STABILITY OF RANDOM MEASURES

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

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.

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.

참고문헌 (17)

  1. R. J. Adler, "A Practical Guide to Heavy Tailed Data" (1998), Birkhauser
  2. Y. Davydov, "Strictly stable distributions on convex cones", Electron. J. Probab, 13(11), pp.259~321 (2008)
  3. Y. Davydov, "Stability for random measures, point processes and discrete semigroups", Bernoulli, 17(3), pp.1015~1043 (2011)
  4. J. L. Geluk, "Stable probability distributions and their domains of attraction: A direct approach", Probab. Math. Statist, 20(1), pp.169~188 (2000)
  5. B. V. Gnedenko, "Limit Distributions for Sum of Independent Random Variables" (1954), Addison-Wesley
  6. H. Hult, "Regular variation for measures on metric spaces", Publ. Inst. Math, 80(94), pp.121~140 (2006)
  7. R. Jajte, "On stable distributions in Hilbert space", Studia Math, 30, pp.63~71 (1968)
  8. O. Kallenberg, "Random Measures" (1983), Akademie-Verlag
  9. A. Kumar, "Stable probability measures on Banach spaces", Studia Math, 42, pp.133~144 (1972)
  10. P. Levy, "Theorie de l’addition des variables aleatoires" (1937), Gauthier-Villars
  11. J. McCulloch, "Handbook of Statistics 14", pp.393~425 (1996), Elsevier Science Publishers
  12. Thu Nguyen Van, "Stable random measures", Acta Math. Vietnam, 4(1), pp.71~75 (1979)
  13. K. J. Palmer, "Modelling cell generation times using the tempered stable distribution", J. Roy. Statist. Soc. Ser. C, 57(4), pp.379~397 (2008)
  14. S. I. Resnik, "Heavy-Tail Phenomena: Probabilistic and Statistical Modeling" (2007), Springer
  15. G. Samorodnitsky, "Stable non-Gaussian random processes" (1994), Chapman and Hall
  16. K. Sato, "Strictly operator-stable distributions", J. Multivariate Anal, 22(2), pp.278~295 (1987)
  17. V. M. Zolotarev, "One-dimensional stable distributions" (1986), American Mathematical Society

관련 논문AI추천

이 간행물의 다른 논문 (20건)