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Subexponentiality and infinite divisibility. (English) Zbl 0397.60024

MSC:
60E05 Probability distributions: general theory
60F99 Limit theorems in probability theory
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[1] Athreya, K.B., Ney, P.E.: Branching Processes. Berlin-Heidelberg-New York: Springer 1972 · 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 ? second edition. New York-London-Sydney-Toronto: John Wiley 1971 · 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. Princeton: University Press 1941 · Zbl 0063.08245
[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
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