References
L. Alpar, “Tauberian theorems for power series of two variables,” Studia Sci. Math. Hungar., 19, 165–176 (1984).
A. Baltrunas and E. Omey, “The rate of convergence for subexponential distributions,” Liet. Matem. Rink., 38, No. 1, 1–18 (1998).
A. Baltrunas and E. Omey, “The rate of convergence for subexponential distributions and densities,” Liet. Matem. Rink., 42, No. 1, 1–18 (2002).
B. Basrak, R. A. Davis, and T. Mikosch, “A characterization of multivariate regular variation,” Ann. Appl. Probab., 12, No. 3, 908–920 (2002).
N. H. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1987).
J. Chover, P. Ney, and S. Wainger, “Functions of probability measures,” J. Anal. Math., 26, 255–302 (1973).
J. Chover, P. Ney, and S. Wainger, “Degeneracy properties of subcritical branching processes,” Ann. Probab., 1, 663–673 (1973).
D. B. H. Cline, “Convolution tails, product tails and domains of attraction,” Probab. Theor. Rel. Fields, 72, 529–557 (1986).
D. B. H. Cline, “Convolutions of distributions with exponential and subexponential tails,” J. Austral. Math. Soc., Ser. A, 43, 347–365 (1987).
D. B. H. Cline and S. I. Resnick, “Multivariate subexponential distributions,” Stoch. Proc. Appl., 42, 49–72 (1992).
P. Embrechts, C. M. Goldie, and N. Veraverbeke, “Subexponentiality and infinite divisibility,” Z. Wahrsch. verw. Geb., 49, 335–347 (1979).
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).
P. Embrechts and C. M. Goldie, “On convolution tails,” Stoch. Proc. Appl., 13, 263–278 (1982).
P. Embrechts, “Subexponential distribution functions and their applications: A review,” in: Proceedings of VII Conference On Probability Theory, Brasov, Roumania (1985), pp. 125–136.
P. Embrechts, C. Kluppelberg, and T. Mikosch, “Modelling extremal events,” Appl. Math. Stoch. Mod. Appl. Probab., 33 (1997).
J. Geluk and L. de Haan, Regular Variation, Extensions, and Tauberian Theorems, Center for Mathematics and Computer Science, Amsterdam (1987).
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).
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).
M. V. Johns, “Nonparametric empirical Bayes procedures,” Ann. Math. Statist., 28, 649–669 (1957).
F. Mallor and E. Omey, “Shocks, runs and random sums,” J. Appl. Probab., 38, 438–448 (2001).
F. Mallor and E. Omey, “Shocks, runs and random sums: Asymptotic behavior of the distribution function,” (2001) (to appear).
F. Mallor, E. Omey, and J. Santos, “Lifetime of series systems subject to shocks,” J. Dependability Quality Management (2003) (to appear).
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).
E. Omey, Multivariate Reguliere Variatie en Toepassingen in kanstheorie, Ph.D. Thesis, K.U.Leuven (1982) (in Dutch).
E. Omey, “Multivariate regular variation and applications in probability theory,” Eclectica, 74 (1989).
E. Omey, “Random sums of random vectors,” Publ. Inst. Math. Béograd, 48, No. 62, 191–198 (1990).
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).
E. Omey, “On a subclass of regularly varying functions,” J. Statist. Planning Inform., 45, 275–290 (1995).
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).
E. Omey, “Subexponential distributions and the difference between the product and the convolution product of distribution functions in R d,” (2003) (forthcoming).
E. Omey and J. L. Teugels, “Weighted renewal functions: A hierarchical approach,” Adv. Appl. Probab., 34, 394–415 (2002).
E. Omey and E. Willekens, “Second-order behavior of the tail of a subordinated probability distribution,” Stoch. Proc. Appl., 21, 339–353 (1986).
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).
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).
J. W. Pratt, “On interchanging limits and integrals,” Ann. Statist., 31, 74–77 (1960).
S. I. Resnick, “Point processes, regular variation and weak convergence,” Adv. Appl. Probab., 18, 66–138 (1986).
S. I. Resnick, Extreme Values, Regular Variation and Point Processes, Springer, New York (1987).
E. Seneta, “Functions of regular variation,” Lect. Note. Math., 506 (1976).
A. Stam, Regular Variation in R +d and the Abel-Tauber Theorem, Preprint, Math. Inst. Rijksuniversiteit Groningen, The Netherlands (1977).
J. L. Teugels, “The class of subexponential distributions,” Ann. Probab., 3, 1000–1011 (1975).
E. Willekens, Higher-Order Theory for Subexponential Distributions, Ph.D. Thesis, K.U.Leuven (1986) (in Dutch).
A. Yakimiv, “Multidimensional Tauberian theorems and the Bellman-Harris process,” Mat. Sbornik, 115, No. 3, 463–477 (1981).
Author information
Authors and Affiliations
Additional information
Proceedings of the Seminar on Stability Problems for Stochastic Models, Pamplona, Spain, 2003
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/s10958-006-0310-8