References

1. Albin, J. M. P. A note on the closure of convolution power mixtures (random sums) of exponential distributions. J. Aust. Math. Soc. 84 (2008), no. 1, 1--7. MR2469263
2. Albin, J. M. P.; Sundén, Mattias. On the asymptotic behaviour of Lévy processes. I. Subexponential and exponential processes. Stochastic Process. Appl. 119 (2009), no. 1, 281--304. MR2485028 (Review)
3. Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation.Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871 (88i:26004)
4. Braverman, Michael. Suprema and sojourn times of Lévy processes with exponential tails. Stochastic Process. Appl. 68 (1997), no. 2, 265--283. MR1454836 (99f:60025)
5. Braverman, Michael. On a class of Lévy processes. Statist. Probab. Lett. 75 (2005), no. 3, 179--189. MR2210548 (2006m:60066)
6. Braverman, Michael; Samorodnitsky, Gennady. Functionals of infinitely divisible stochastic processes with exponential tails. Stochastic Process. Appl. 56 (1995), no. 2, 207--231. MR1325220 (96e:60063)
7. Cline, Daren B. H. Convolutions of distributions with exponential and subexponential tails. J. Austral. Math. Soc. Ser. A 43 (1987), no. 3, 347--365. MR0904394 (89a:60049)
8. Cohen, J. W. Some results on regular variation for distributions in queueing and fluctuation theory. J. Appl. Probability 10 (1973), 343--353. MR0353491 (50 #5974)
9. Denisov, Denis; Foss, Serguei; Korshunov, Dmitry. On lower limits and equivalences for distribution tails of randomly stopped sums. Bernoulli 14 (2008), no. 2, 391--404. MR2544093
10. Embrechts, Paul; Goldie, Charles M. On closure and factorization properties of subexponential and related distributions. J. Austral. Math. Soc. Ser. A 29 (1980), no. 2, 243--256. MR0566289 (81j:60019)
11. Embrechts, Paul; Goldie, Charles M. Comparing the tail of an infinitely divisible distribution with integrals of its Lévy measure. Ann. Probab. 9 (1981), no. 3, 468--481. MR0614631 (82i:60033)
12. Embrechts, Paul; Goldie, Charles M. On convolution tails. Stochastic Process. Appl. 13 (1982), no. 3, 263--278. MR0671036 (84a:60027)
13. Embrechts, Paul; Goldie, Charles M.; Veraverbeke, Noël. Subexponentiality and infinite divisibility. Z. Wahrsch. Verw. Gebiete 49 (1979), no. 3, 335--347. MR0547833 (80j:60025)
14. Embrechts, Paul; Hawkes, John. A limit theorem for the tails of discrete infinitely divisible laws with applications to fluctuation theory. J. Austral. Math. Soc. Ser. A 32 (1982), no. 3, 412--422. MR0652419 (83m:60093)
15. Embrechts, Paul; Klüppelberg, Claudia; Mikosch, Thomas. Modelling extremal events.For insurance and finance.Applications of Mathematics (New York), 33. Springer-Verlag, Berlin, 1997. xvi+645 pp. ISBN: 3-540-60931-8 MR1458613 (98k:60080)
16. Feller, William. One-sided analogues of Karamata's regular variation. Enseignement Math. (2) 15 1969 107--121. MR0254905 (40 #8112)
17. Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403 (42 #5292)
18. Foss, Serguei; Korshunov, Dmitry. Lower limits and equivalences for convolution tails. Ann. Probab. 35 (2007), no. 1, 366--383. MR2303954 (2007k:60045)
19. Goldie, Charles M. Subexponential distributions and dominated-variation tails. J. Appl. Probability 15 (1978), no. 2, 440--442. MR0474459 (57 #14099)
20. de Haan, L.; Stadtmüller, U. Dominated variation and related concepts and Tauberian theorems for Laplace transforms. J. Math. Anal. Appl. 108 (1985), no. 2, 344--365. MR0793651 (86k:44002)
21. Klüppelberg, Claudia; Kyprianou, Andreas E.; Maller, Ross A. Ruin probabilities and overshoots for general Lévy insurance risk processes. Ann. Appl. Probab. 14 (2004), no. 4, 1766--1801. MR2099651 (2005j:60097)
22. Klüppelberg, Claudia; Villaseñor, José A. The full solution of the convolution closure problem for convolution-equivalent distributions. J. Math. Anal. Appl. 160 (1991), no. 1, 79--92. MR1124078 (92m:60018)
23. Leslie, J. R. On the nonclosure under convolution of the subexponential family. J. Appl. Probab. 26 (1989), no. 1, 58--66. MR0981251 (90a:60025)
24. Pakes, Anthony G. Convolution equivalence and infinite divisibility. J. Appl. Probab. 41 (2004), no. 2, 407--424. MR2052581 (2005b:60037)
25. Rudin, Walter. Limits of ratios of tails of measures. Ann. Probability 1 (1973), 982--994. MR0358919 (50 #11376)
26. Sato. K. Levy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge 1999.
27. Shimura, Takaaki; Watanabe, Toshiro. Infinite divisibility and generalized subexponentiality. Bernoulli 11 (2005), no. 3, 445--469. MR2146890 (2006a:62028)
28. T. Shimura, T. Watanabe. On the convolution roots in the convolution-equivalent class. The Institute of Statistical Mathematics Cooperative Research Report 175 (2005), pp1-15.
29. Teugels, Jozef L. The class of subexponential distributions. Ann. Probability 3 (1975), no. 6, 1000--1011. MR0391222 (52 #12043)
30. Watanabe, Toshiro. Sample function behavior of increasing processes of class $L$. Probab. Theory Related Fields 104 (1996), no. 3, 349--374. MR1376342 (97e:60125)
31. Watanabe, Toshiro. Convolution equivalence and distributions of random sums. Probab. Theory Related Fields 142 (2008), no. 3-4, 367--397. MR2438696 (2009j:60031)
32. Watanabe, Toshiro: Yamamuro, Kouji. Local subexponentiality and self-decomposability. to appear in J. Theoret. Probab. (2010).
33. Yakymiv, A. L. Asymptotic behavior of a class of infinitely divisible distributions.(Russian) Teor. Veroyatnost. i Primenen. 32 (1987), no. 4, 691--702. MR0927250 (89d:60027)