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Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries

  • Anthony G. Pakes (a1)

Abstract

Corrections are made to formulations and proofs of some theorems about convolution equivalence closure for random sum distributions. These arise because of the falsity of a much used asymptotic equivalence lemma, and they impinge on the convolution equivalence closure theorem for general infinitely divisible laws.

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Copyright

Corresponding author

Postal address: Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. Email address: pakes@maths.uwa.edu.au

References

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Chover, J., Ney, P. and Wainger, S. (1973). Degeneracy properties of subcritical branching processes. Ann. Prob. 1, 663673.
Cline, D. B. H. (1987). Convolutions of distributions with exponential and subexponential tails. J. Austral. Math. Soc. Ser. A 43, 347365. (Correction: 48, (1990), 152–153.)
Embrechts, P. and Goldie, C. M. (1982). On convolution tails. Stoch. Process. Appl. 13, 263278.
Foss, S. and Korshunov, D. (2007). Lower limits and equivalences for convolution tails. Ann. Prob. 35, 366383
Goldie, C. M. and Klüppelberg, C. (1998). Subexponential distributions. In A Practical Guide to Heavy Tails, eds Adler, R., Feldman, R. and Taqqu, M. S., Birkhäuser, Boston, MA, pp. 435459.
Klüppelberg, C. (1989). Subexponential distributions and characterizations of related classes. Prob. Theory Relat. Fields 82, 259269.
Pakes, A. G. (2004). Convolution equivalence and infinite divisibility. J. Appl. Prob. 41, 407424.
Rogozin, B. A. (2000). On the constant in the definition of subexponential distributions. Theory Prob. Appl. 44, 409412.
Rogozin, B. A. and Sgibnev, M. S. (1999). Strongly exponential distributions, and Banach algebras of measures. Siberian Math. J. 40, 963971.
Shimura, T. and Watanabe, T. (2005). Infinite divisibility and generalized subexponentiality. Bernoulli 11, 445469.
Wang, Y., Yang, Y., Wang, K. and Cheng, D. (2007). Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications. Insurance Math. Econom. 40, 256266.
Watanabe, T. (2007). Convolution equivalence and distributions of random sums of IID. Submitted.
Willekens, E. (1987). Subexponentiality on the real line. Res. Rep., Katholieke Universiteit Leuven.

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