[1] Kl¨uppelberg C, Mikosch T. Large deviations of heavy-tailed random sums with applications in insurance and finance. Adv Appl Probab, 1997, 34: 293–308
[2] Nagaev A V. Integral limit theorems for large deviations when Cram´er’s condition is not fulfilled I, II.Theory Probab Appl, 1969, 14: 51–64; 193–208
[3] Nagaev S V. Large deviations of sums of independent random variables. Ann Probab, 1979, 7: 745–789
[4] Cline D B H, Hsing T. Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Preprint, Texas A&M University, 1991
[5] Kong F, Tang Q. A theorem on the convergence of sums of independent random variables. Acta Mathematica Scientia, 2001, 21(3): 331–338
[6] Tang Q, et al. Large deviations for heavy-tailed random sums in compound renewal model. Statist Probab Lett, 2001, 52: 91–100
[7] Ng K W, et al. Precise large deviations for sums of random variables with consistently varying tails. J Appl Probab, 2004, 41: 93–107
[8] Wang D, Tang Q. Maxima of sums and random sums for negatively associated random variables with heavy tails. Statist Probab Lett, 2004, 68: 287–295
[9] Tang Q. Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electron J Probab, 2006, 11: 107–120
[10] Paulauskas V, Skuˇcait˙e A. Some asymptotic results for one-sided large deviation probabilities. Lith Math J, 2003, 43(3): 318–326
[11] Skuˇcait˙e A. Large deviations for sums of independent heavy-tailed random variables. Lith Math J, 2004, 44(2): 198–208
[12] Gao F Q. Moderate deviations for random sums of heavy-tailed random variables. Acta Math Sin (Engl Ser), 2007, 23(8): 1527–1536
[13] Embrechts P, Kl¨uppelberg C, Mikosch T. Modelling Extremal Events for Insurance and Finance. Berlin, Heidelberg: Springer, 1997
[14] Meerschaert M M, Scheffler H P. Limit Distributions for Sums of Independent Random Vectors. Heavy Tails in Theory and Practice. New York: Wiley, 2001
[15] Tang Q, Tsitsiashvili G. Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. Stochastic Process Appl, 2003, 108: 299–325
[16] Liu L. Precise large deviations for dependent random variables with heavy tails. Statist Probab Lett, 2009, 79: 1290–1298
[17] Liu L. Necessary and sufficient conditions for moderate deviations of dependent random variables with heavy tails. Sci China Ser A, 2010, 53: 1421–1434 |