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Subexponential distribution functions in Rd

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References

  1. L. Alpar, “Tauberian theorems for power series of two variables,” Studia Sci. Math. Hungar., 19, 165–176 (1984).

    MATH  MathSciNet  Google Scholar 

  2. A. Baltrunas and E. Omey, “The rate of convergence for subexponential distributions,” Liet. Matem. Rink., 38, No. 1, 1–18 (1998).

    MATH  MathSciNet  Google Scholar 

  3. A. Baltrunas and E. Omey, “The rate of convergence for subexponential distributions and densities,” Liet. Matem. Rink., 42, No. 1, 1–18 (2002).

    MATH  MathSciNet  Google Scholar 

  4. B. Basrak, R. A. Davis, and T. Mikosch, “A characterization of multivariate regular variation,” Ann. Appl. Probab., 12, No. 3, 908–920 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  5. N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1987).

    MATH  Google Scholar 

  6. J. Chover, P. Ney, and S. Wainger, “Functions of probability measures,” J. Anal. Math., 26, 255–302 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  7. J. Chover, P. Ney, and S. Wainger, “Degeneracy properties of subcritical branching processes,” Ann. Probab., 1, 663–673 (1973).

    MATH  MathSciNet  Google Scholar 

  8. D. B. H. Cline, “Convolution tails, product tails and domains of attraction,” Probab. Theor. Rel. Fields, 72, 529–557 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  9. D. B. H. Cline, “Convolutions of distributions with exponential and subexponential tails,” J. Austral. Math. Soc., Ser. A, 43, 347–365 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  10. D. B. H. Cline and S. I. Resnick, “Multivariate subexponential distributions,” Stoch. Proc. Appl., 42, 49–72 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  11. P. Embrechts, C. M. Goldie, and N. Veraverbeke, “Subexponentiality and infinite divisibility,” Z. Wahrsch. verw. Geb., 49, 335–347 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  12. P. Embrechts and C. M. Goldie, “On closure and factorization properties of subexponential and related distributions,” J. Austral. Math. Soc., Ser. A, 29, 243–256 (1980).

    MATH  MathSciNet  Google Scholar 

  13. P. Embrechts and C. M. Goldie, “On convolution tails,” Stoch. Proc. Appl., 13, 263–278 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  14. P. Embrechts, “Subexponential distribution functions and their applications: A review,” in: Proceedings of VII Conference On Probability Theory, Brasov, Roumania (1985), pp. 125–136.

  15. P. Embrechts, C. Kluppelberg, and T. Mikosch, “Modelling extremal events,” Appl. Math. Stoch. Mod. Appl. Probab., 33 (1997).

  16. J. Geluk and L. de Haan, Regular Variation, Extensions, and Tauberian Theorems, Center for Mathematics and Computer Science, Amsterdam (1987).

    MATH  Google Scholar 

  17. L. de Haan and E. Omey, “Integrals and derivatives of regularly varying functions in R d and domains of attraction of stable distributions, II,” Stoch. Proc. Appl., 16, 157–170 (1983).

    Article  Google Scholar 

  18. L. de Haan, E. Omey, and S. I. Resnick, “Domains of attraction and regular variation in R d,” J. Multiv. Anal., 14, 17–33 (1984).

    Article  MATH  Google Scholar 

  19. M. V. Johns, “Nonparametric empirical Bayes procedures,” Ann. Math. Statist., 28, 649–669 (1957).

    MATH  MathSciNet  Google Scholar 

  20. F. Mallor and E. Omey, “Shocks, runs and random sums,” J. Appl. Probab., 38, 438–448 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  21. F. Mallor and E. Omey, “Shocks, runs and random sums: Asymptotic behavior of the distribution function,” (2001) (to appear).

  22. F. Mallor, E. Omey, and J. Santos, “Lifetime of series systems subject to shocks,” J. Dependability Quality Management (2003) (to appear).

  23. F. Mallor, E. Omey, and J. Santos, “Comportamiento asintotico de un modelo de fiabilidad mixto acumulado y de rachas de shocks,” in: XXVII Congreso Nacional de Estadistica e Investigacion Operativa, Lleida (2003).

  24. E. Omey, Multivariate Reguliere Variatie en Toepassingen in kanstheorie, Ph.D. Thesis, K.U.Leuven (1982) (in Dutch).

  25. E. Omey, “Multivariate regular variation and applications in probability theory,” Eclectica, 74 (1989).

  26. E. Omey, “Random sums of random vectors,” Publ. Inst. Math. Béograd, 48, No. 62, 191–198 (1990).

    MATH  MathSciNet  Google Scholar 

  27. E. Omey, “On the difference between the product and the convolution product of distribution functions,” Publ. Inst. Math. Béograd, 55, No. 69, 111–145 (1994).

    MATH  MathSciNet  Google Scholar 

  28. E. Omey, “On a subclass of regularly varying functions,” J. Statist. Planning Inform., 45, 275–290 (1995).

    Article  MATH  MathSciNet  Google Scholar 

  29. E. Omey, “On the difference between the distribution function of the sum and the maximum of real random variables,” Publ. Inst. Math. B’eograd, 71, No. 85, 63–77 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  30. E. Omey, “Subexponential distributions and the difference between the product and the convolution product of distribution functions in R d,” (2003) (forthcoming).

  31. E. Omey and J. L. Teugels, “Weighted renewal functions: A hierarchical approach,” Adv. Appl. Probab., 34, 394–415 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  32. E. Omey and E. Willekens, “Second-order behavior of the tail of a subordinated probability distribution,” Stoch. Proc. Appl., 21, 339–353 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  33. E. Omey and E. Willekens, “Second-order behavior of distributions subordinate to a distribution with finite mean,” Comm. Statist. Stoch. Mod., 3, No. 3, 311–342 (1987).

    MATH  MathSciNet  Google Scholar 

  34. E. Omey and E. Willekens, “Abelian and Tauberian theorems for the Laplace transform of functions in several variables,” J. Multiv. Anal., 30, 292–306 (1988).

    Article  MathSciNet  Google Scholar 

  35. J. W. Pratt, “On interchanging limits and integrals,” Ann. Statist., 31, 74–77 (1960).

    MATH  MathSciNet  Google Scholar 

  36. S. I. Resnick, “Point processes, regular variation and weak convergence,” Adv. Appl. Probab., 18, 66–138 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  37. S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Springer, New York (1987).

    MATH  Google Scholar 

  38. E. Seneta, “Functions of regular variation,” Lect. Note. Math., 506 (1976).

  39. A. Stam, Regular Variation in R +d and the Abel-Tauber Theorem, Preprint, Math. Inst. Rijksuniversiteit Groningen, The Netherlands (1977).

    Google Scholar 

  40. J. L. Teugels, “The class of subexponential distributions,” Ann. Probab., 3, 1000–1011 (1975).

    MATH  MathSciNet  Google Scholar 

  41. E. Willekens, Higher-Order Theory for Subexponential Distributions, Ph.D. Thesis, K.U.Leuven (1986) (in Dutch).

  42. A. Yakimiv, “Multidimensional Tauberian theorems and the Bellman-Harris process,” Mat. Sbornik, 115, No. 3, 463–477 (1981).

    Google Scholar 

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Proceedings of the Seminar on Stability Problems for Stochastic Models, Pamplona, Spain, 2003

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Omey, E.A.M. Subexponential distribution functions in Rd . J Math Sci 138, 5434–5449 (2006). https://doi.org/10.1007/s10958-006-0310-8

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