Convolutions of long-tailed and subexponential distributions

Convolutions of long-tailed and subexponential distributions

Foss Sergey, Korshunov Dmitry, and Zachary Stan

Source: J. Appl. Probab. Volume 46, Number 3 (2009), 756-767.

Abstract

Convolutions of long-tailed and subexponential distributions play a major role in the analysis of many stochastic systems. We study these convolutions, proving some important new results through a simple and coherent approach, and also showing that the standard properties of such convolutions follow as easy consequences.

Primary Subjects: 60E05

Secondary Subjects: 60F10, 60G70

Keywords: Long-tailed distribution; subexponential distribution

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.jap/1253279850
Digital Object Identifier: doi:10.1239/jap/1253279850
Zentralblatt MATH identifier: 05611416

back to Table of Contents

References

Asmussen, S. (2000). Ruin Probabilities. World Scientific, River Edge, NJ.

Mathematical Reviews (MathSciNet): MR1794582

Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.

Mathematical Reviews (MathSciNet): MR1978607

Asmussen, A., Foss, S. and Korshunov, D. (2003). Asymptotics for sums of random variables with local subexponential behaviour. J. Theoret. Prob. 16, 489--518.

Mathematical Reviews (MathSciNet): MR1982040

Zentralblatt MATH: 1033.60053

Digital Object Identifier: doi:10.1023/A:1023535030388

Athreya, K. B. and Ney, P. E. (1972). Branching Processes. Springer, New York.

Mathematical Reviews (MathSciNet): MR373040

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

Mathematical Reviews (MathSciNet): MR898871

Chistyakov, V. P. (1964). A theorem on sums of independent positive random variables and its application to branching random processes. Theory Prob. Appl. 9, 640--648.

Mathematical Reviews (MathSciNet): MR170394

Cline, D. B. H. (1987). Convolutions of distributions with exponential and subexponential tails. J. Austral. Math. Soc. 43, 347--365.

Mathematical Reviews (MathSciNet): MR904394

Digital Object Identifier: doi:10.1017/S1446788700029633

Embrechts, P. and Goldie, C. M. (1980). On closure and factorization properties of subexponential and related distributions. J. Austral. Math. Soc. 29, 243--256.

Mathematical Reviews (MathSciNet): MR566289

Digital Object Identifier: doi:10.1017/S1446788700021224

Embrechts, P. and Goldie, C. M. (1982). On convolution tails. Stoch. Process. Appl. 13, 263--278.

Mathematical Reviews (MathSciNet): MR671036

Zentralblatt MATH: 0487.60016

Digital Object Identifier: doi:10.1016/0304-4149(82)90013-8

Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979). Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth. 49, 335--347.

Mathematical Reviews (MathSciNet): MR547833

Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events. Springer, Berlin.

Mathematical Reviews (MathSciNet): MR1458613

Klüppelberg, C. (1988). Subexponential distributions and integrated tails. J. Appl. Prob. 25, 132--141.

Mathematical Reviews (MathSciNet): MR929511

Zentralblatt MATH: 0651.60020

Digital Object Identifier: doi:10.2307/3214240

JSTOR: links.jstor.org

Landau, E. (1911). Sur les valeurs moyennes de certaines fonctions arithmétiques. Bull. Acad. Roy. Belgique, 443--472.

Pakes, A. G. (1975). On the tails of waiting-time distributions. J. Appl. Prob. 12, 555--564.

Mathematical Reviews (MathSciNet): MR386056

Zentralblatt MATH: 0314.60072

Digital Object Identifier: doi:10.2307/3212870

JSTOR: links.jstor.org

Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1998). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.

Mathematical Reviews (MathSciNet): MR1680267

Teugels, J. L. (1975). The class of subexponential distributions. Ann. Prob. 3, 1000--1011.

Mathematical Reviews (MathSciNet): MR391222

Digital Object Identifier: doi:10.1214/aop/1176996225

previous :: next