## On convolution tails.(English)Zbl 0487.60016

### MSC:

 60E05 Probability distributions: general theory 60F99 Limit theorems in probability theory 60K05 Renewal theory 60G50 Sums of independent random variables; random walks

### Citations:

Zbl 0374.60022; Zbl 0353.60073
Full Text:

### References:

 [1] Bingham, N.H.; Goldie, C.M., Extensions of regular variation part I: uniformity and quantifiers, (1979), University of London, Westfield College, preprint [2] Chistyakov, V.P., A theorem on sums of independent positive random variables and its applications to branching processes, Theory probab. appl., 9, 640-648, (1964) [3] Chover, J.; Ney, P.; Wainger, S., Functions of probability measures, J. analyse math., 26, 255-302, (1973) · Zbl 0276.60018 [4] Chover, J.; Ney, P.; Wainger, S., Degeneracy properties of subcritical branching processes, Ann. probab., 1, 663-673, (1973) · Zbl 0387.60097 [5] Cohen, J.W., Some results on regular variation for distributions in queueing and fluctuation theory, J. appl. probab., 10, 343-353, (1973) · Zbl 0258.60076 [6] Embrechts, P.; Goldie, C.M., On closure and factorization properties of subexponential and related distributions, J. austral. math. soc. ser. A, 29, 243-256, (1980) · Zbl 0425.60011 [7] Embrechts, P.; Goldie, C.M., Comparing the tail of an infinitely divisible distribution with integrals of its Lévy measure, Ann. probab., 9, 468-481, (1981) · Zbl 0459.60017 [8] embrechts, P.; Goldie, C.M.; Veraverbeke, N., Subexponentiality and infinite divisibility, Z. wahrsch. verw. gabiete, 49, 335-347, (1979) · Zbl 0397.60024 [9] Feller, W., () [10] Pakes, A.G., On the tails of waiting time distributions, J. appl. probab., 15, 555-564, (1975) · Zbl 0314.60072 [11] Rudin, W., Limits of ratios of tails of measures, Ann. probab., 1, 982-984, (1973) · Zbl 0303.60014 [12] Seneta, E., Regularly varying functions, () · Zbl 0291.60043 [13] Smith, W., On the tails of queueing-time distributions, () [14] Stam, A.J., Regular variation of the tail of a subordinated probability distribution, Adv. appl. probab., 5, 308-327, (1972) · Zbl 0264.60029 [15] Steutel, F.W., On the tails of infinitely divisible distributions, Z. wahrsch. verw. gebiete, 28, 273-276, (1974) · Zbl 0269.60016 [16] Teugels, J.L., The class of subexponential distributions, Ann. probab., 3, 1000-1011, (1975) · Zbl 0374.60022 [17] van Aardenne-Ehrenfest, T.; de Bruijn, N.G.; Korevaar, J., A note on slowly oscillating functions, Nieuw arch. wisk., 23, 2, 77-86, (1949) · Zbl 0045.33503 [18] Veraverbeke, N., Asymptotic behaviour of wiener—hopf factors of a random walk, Stochastic process. appl., 5, 27-37, (1977) · Zbl 0353.60073
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