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Embrechts, Paul; Goldie, Charles M.; Veraverbeke, Noel

Subexponentiality and infinite divisibility. (English) Zbl 0397.60024

Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 335-347 (1979).
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Cited in 3 Reviews
Cited in 151 Documents

MSC:

60E05 Probability distributions: general theory
60F99 Limit theorems in probability theory

Keywords:

Lognormal Distribution; Regular Variation; Subexponential; Compound Poisson; Infinite Divisibility; Closure Properties; Factorization Properties
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\textit{P. Embrechts} et al., Z. Wahrscheinlichkeitstheor. Verw. Geb. 49, 335--347 (1979; Zbl 0397.60024)
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References:

[1] Athreya, K. B.; Ney, P. E., Branching Processes (1972), Berlin-Heidelberg-New York: Springer, Berlin-Heidelberg-New York · Zbl 0259.60002
[2] Bondesson, L.: A general result on infinite divisibility. [To appear in Ann. Probability] · Zbl 0421.60014
[3] Callaert, H.; Cohen, J. W., A lemma on regular variation of a transient renewal function, Z. Wahrscheinlichkeitstheorie und verw. Gebiete, 24, 275-278 (1972) · Zbl 0237.60036
[4] Chistyakov, V. P., A theorem on sums of independent, positive random variables and its applications to branching processes, Theory Probability Appl., 9, 640-648 (1964)
[5] Chover, J.; Ney, P.; Wainger, S., Degeneracy properties of subcritical branching processes, Ann. Probability, 1, 663-673 (1973) · Zbl 0387.60097
[6] Chover, J.; Ney, P.; Wainger, S., Functions of probability measures, J. Analyse Math., 26, 255-302 (1973) · Zbl 0276.60018
[7] Cohen, J. W., Some results on regular variation for distributions in queueing and fluctuation theory, J. Appl. Probability, 10, 343-353 (1973) · Zbl 0258.60076
[8] Feller, W., One sided analogues of Karamata’s regular variation, Enseignement Math., 15, 107-121 (1969) · Zbl 0177.08201
[9] Feller, W., An introduction to Probability theory and its Applications. Vol. II (1971), New York-London-Sydney-Toronto: John Wiley, New York-London-Sydney-Toronto · Zbl 0219.60003
[10] Goldie, C. M., Subexponential distributions and dominated-variation tails, J. Appl. Probability, 15, 440-442 (1978) · Zbl 0378.60009
[11] Pakes, A. G., On the tails of waiting time distributions, J. Appl. Probability, 12, 555-564 (1975) · Zbl 0314.60072
[12] Stam, A. J., Regular variation of the tail of a subordinated probability distribution, Adv. Appl. Probability, 5, 308-327 (1973) · Zbl 0264.60029
[13] Teugels, J. L., The class of subexponential distributions, Ann. Probability, 3, 1000-1011 (1975) · Zbl 0374.60022
[14] Thorin, O.: On the infinite divisibility of the lognormal distribution. Scand. Actuarial J. 121-148 (1977) · Zbl 0372.60020
[15] Veraverbeke, N., Asymptotic behaviour of Wiener-Hopf factors of a random walk, Stochastic Processes Appl., 5, 27-37 (1977) · Zbl 0353.60073
[16] Widder, D. V., The Laplace transform (1941), Princeton: University Press, Princeton · JFM 67.0384.01
[17] Zolotarev, V. M., On the asymptotic behaviour of a class of infinitely divisible laws, Theory Probability Appl., 6, 304-307 (1961) · Zbl 0124.34501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.