References

1. Alam, Khursheed; Saxena, K. M. Lal. Positive dependence in multivariate distributions. Comm. Statist. A---Theory Methods 10 (1981), no. 12, 1183--1196. MR0623526 (83a:62114)
2. Baltrunas, Aleksandras; Klüppelberg, Claudia. Subexponential distributions---large deviations with applications to insurance and queueing models. Festschrift in honour of Daryl Daley. Aust. N. Z. J. Stat. 46 (2004), no. 1, 145--154. MR2060959 (2005c:60028)
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. Bingham, N. H.; Nili Sani, H. R. Summability methods and negatively associated random variables. Stochastic methods and their applications. J. Appl. Probab. 41A (2004), 231--238. MR2057576 (2005e:60066)
5. Block, Henry W.; Savits, Thomas H.; Shaked, Moshe. Some concepts of negative dependence. Ann. Probab. 10 (1982), no. 3, 765--772. MR0659545 (83i:60015)
6. Cai, Jun; Tang, Qihe. On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications. J. Appl. Probab. 41 (2004), no. 1, 117--130. MR2036276 (2004k:60030)
7. Cline, Daren B. H. Intermediate regular and $\Pi$ variation. Proc. London Math. Soc. (3) 68 (1994), no. 3, 594--616. MR1262310 (95c:26001)
8. Cline, Daren B. H. ; T. Hsing. Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint (1991), Texas A\&M University.
9. Cline, D. B. H.; Samorodnitsky, G. Subexponentiality of the product of independent random variables. Stochastic Process. Appl. 49 (1994), no. 1, 75--98. MR1258283 (94m:60029)
10. Ebrahimi, Nader; Ghosh, Malay. Multivariate negative dependence. Comm. Statist. A---Theory Methods 10 (1981), no. 4, 307--337. MR0612400 (83a:62125)
11. Fuk, D. H.; Nagaev, S. V. Probabilistic inequalities for sums of independent random variables. (Russian) Teor. Verojatnost. i Primenen. 16 (1971), 660--675. MR0293695 (45 #2772)
12. Heyde, C. C. A contribution to the theory of large deviations for sums of independent random variables. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 7 1967 303--308. MR0216549 (35 #7380)
13. Heyde, C. C. On large deviation problems for sums of random variables which are not attracted to the normal law. Ann. Math. Statist. 38 1967 1575--1578. MR0221564 (36 #4616)
14. Heyde, C. C. On large deviation probabilities in the case of attraction to a non-normal stable law. Sankhy\=a Ser. A 30 1968 253--258. MR0240854 (39 #2199)
15. Joag-Dev, Kumar; Proschan, Frank. Negative association of random variables, with applications. Ann. Statist. 11 (1983), no. 1, 286--295. MR0684886 (85d:62058)
16. Kotz, Samuel; Balakrishnan, N.; Johnson, Norman L.. Continuous multivariate distributions. Vol. 1. Models and applications. Second edition. Wiley Series in Probability and Statistics: Applied Probability and Statistics. Wiley-Interscience, New York, 2000. xxii+722 pp. ISBN: 0-471-18387-3 MR1788152 (2001h:62001)
17. Lehmann, E. L. Some concepts of dependence. Ann. Math. Statist. 37 1966 1137--1153. MR0202228 (34 #2101)
18. Mikosch, T.; Nagaev, A. V. Large deviations of heavy-tailed sums with applications in insurance. Extremes 1 (1998), no. 1, 81--110. MR1652936 (99i:60057)
19. Nagaev, A. V. Integral limit theorems with regard to large deviations when Cramér's condition is not satisfied. I. (Russian) Teor. Verojatnost. i Primenen. 14 1969 51--63. MR0247651 (40 #915a)
20. Nagaev, A. V. Integral limit theorems with regard to large deviations when Cramer's condition is not satisfied. II. Theory Probab. Appl. 14 (1969b), 193--208.
21. Nagaev, A. V. Limit theorems that take into account large deviations when Cramér's condition is violated. (Russian) Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk 13 1969 no. 6, 17--22. MR0282396 (43 #8108)
22. Nagaev, S. V. Large deviations for sums of independent random variables. Transactions of the Sixth Prague Conference on Information Theory, Statistical Decision Functions, Random Processes (Tech. Univ., Prague, 1971; dedicated to the memory of Antonín \v Spa\v cek), pp. 657--674. Academia, Prague, 1973. MR0362460 (50 #14901)
23. Nagaev, S. V. Large deviations of sums of independent random variables. Ann. Probab. 7 (1979), no. 5, 745--789. MR0542129 (80i:60032)
24. Ng, Kai W.; Tang, Qihe; Yan, Jia-An; Yang, Hailiang. Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab. 41 (2004), no. 1, 93--107. MR2036274 (2005j:60053)
25. Pinelis, I. F. Asymptotic equivalence of the probabilities of large deviations for sums and maximum of independent random variables. (Russian) Limit theorems of probability theory, 144--173, 176, Trudy Inst. Mat., 5, "Nauka" Sibirsk. Otdel., Novosibirsk, 1985. MR0821760 (87k:60086)
26. Rozovski\u\i, L. V. Probabilities of large deviations on the whole axis. (Russian) Teor. Veroyatnost. i Primenen. 38 (1993), no. 1, 79--109; translation in Theory Probab. Appl. 38 (1993), no. 1, 53--79 MR1317784 (95m:60052)
27. Stadtmüller, U.; Trautner, R. Tauberian theorems for Laplace transforms. J. Reine Angew. Math. 311/312 (1979), 283--290. MR0549970 (81f:44006)
28. Tang, Qihe; Su, Chun; Jiang, Tao; Zhang, Jinsong. Large deviations for heavy-tailed random sums in compound renewal model. Statist. Probab. Lett. 52 (2001), no. 1, 91--100. MR1820135 (2001k:60040)
29. Tang, Qihe; Tsitsiashvili, Gurami. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Process. Appl. 108 (2003), no. 2, 299--325. MR2019056 (2004h:62189)
30. Tang, Qihe; Yan, Jia'an. A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails. Sci. China Ser. A 45 (2002), no. 8, 1006--1011. MR1942914 (2003i:60029)
31. Vinogradov, Vladimir. Refined large deviation limit theorems. Pitman Research Notes in Mathematics Series, 315. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994. xii+212 pp. ISBN: 0-582-25499-X MR1312369 (96d:60040)