Precise large deviations for the difference of two sums of WUOD and non identically distributed random variables with dominatedly varying tails

References

• Bingham, N.H., Goldie, C.M., Teugels, J.L. (1987). Regular Variation. New York, NY: Cambridge University Press.
   Google Scholar
• Block, H.W., Savits, T.H., Shaked, M. (1982). Some concepts of negative dependence. Ann. Probab. 10:765–772.
   Web of Science ®Google Scholar
• Chen, Y., Yuen, K.C., Ng, K.W. (2011). Precise large deviations of random sums in presence of negative dependence and consistent variation. Methodol. Comput. Appl. Probab. 13(4):821–833.
   Web of Science ®Google Scholar
• Cline, D.B.H., Hsing, T. (1991). Large deviation probabilities for sums and maxima of random variables with heavy or subexponential tails. Texas AM University. Preprint.
   Google Scholar
• Cline, D.B.H., Samorodnitsky, G. (1994). Subexponentiality of the product of independent random variables. Stoch. Process. Appl. 49:75–98.
   Web of Science ®Google Scholar
• He, W., Cheng, D., Wang, Y. (2013). Asymptotic lower bounds of precise large deviations with nonnegative and dependent random variables. Stat. Probab. Lett. 83:331–338.
   Web of Science ®Google Scholar
• Klüppelberg, C., Mikosch, T. (1997). Large deviations of heavy-tailed random sums with applications in insurance and finance. J. Appl. Probab. 34:293–308.
   Web of Science ®Google Scholar
• Liu, L. (2009). Precise large deviations for dependent random variables with heavy tails. Stat. Probab. Lett. 79:1290–1298.
   Web of Science ®Google Scholar
• Lu, D. (2011). Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model. Stat. Probab. Lett. 81:1911–1919.
   Web of Science ®Google Scholar
• Lu, D. (2012). Lower bounds of large deviation for sums of long-tailed claims in a multi-risk model. Stat. Probab. Lett. 82:1242–1250.
   Web of Science ®Google Scholar
• Lu, D., Song, L., Wang, X. (2013). Precise large deviations for the difference of two sums of random variables. Accepted.
   Google Scholar
• Lu, D., Song, L., Xu, Y. (2014). Precise large deviations for sums of independent random variables with consistently varying tails. Commun. Stat. Theory Methods 43:28–43.
   Web of Science ®Google Scholar
• Ng, K.W., Tang, Q., Yan, J., Yang, H. (2004). Precise large deviations for sums of random variables with consistently varying tails. J. Appl. Probab. 41:93–107.
   Web of Science ®Google Scholar
• Skučaitė, A., (2004). Large deviations for sums of independent heavy-tailed random variables. Lith. Math. J. 44(2):198–208.
   Google Scholar
• Tang, Q. (2004). The ruin probability of a discrete time risk model under constant interest rate with heavy tails. Scand. Actuar. J. 2004(3):229–240.
   Google Scholar
• Tang, Q. (2006). Insensitivity to negative dependence of the asymptotic behavior of precise large deviations. Electron. J. Probab. 11(4):107–120.
   Web of Science ®Google Scholar
• Tang, Q., Su, C., Jiang, T., Zhang, J. (2001). Large deviations for heavy-tailed random sums in compound renewal model. Stat. Probab. Lett. 52:91–100.
   Web of Science ®Google Scholar
• Tang, Q., Tsitsiashvili, G. (2003). Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy tailed insurance and financial risks. Stochastic Process. Appl. 108:299–325.
   Web of Science ®Google Scholar
• Wang, K., Wang, Y., Gao, Q. (2013). Uniform asymptotics for the finite-time ruin probability of a dependent risk model with a constant interest rate. Methodol. Comput. Appl. Probab. 15:109–124.
   Web of Science ®Google Scholar
• Wang, K., Yang, Y., Lin, J., (2012). Precise large deviations for widely orthant dependent random variables with dominatedly varying tails. Front. Math. China 7(5):919–932.
   Web of Science ®Google Scholar
• Wang, S., Wang, W. (2007). Precise large deviations for sums of random variables with consistently varying tails in multi-risk models. J. Appl. Probab. 44:889–900.
   Web of Science ®Google Scholar
• Wang, Y., Cheng, D. (2011). Basic renewal theorems for random walks with widely dependent increments. J. Math. Anal. Appl. 384:597–606.
   Web of Science ®Google Scholar
• Wang, Y., Cui, Z., Wang, K., Ma, X. (2012). Uniform asymptotics of the finite-time ruin probability for all times. J. Math. Anal. Appl. 390:208–223.
   Web of Science ®Google Scholar
• Wang, Y., Wang, K., Cheng, D. (2006). Precise large deviations for sums of negatively associated random variables with common dominatedly varying tails. Acta Math. Sin. (Engl. Ser.) 22(6):1725–1734.
   Web of Science ®Google Scholar
• Yang, Y., Wang, K. (2013). Precise large deviations for dependent random variables with applications to the compound renewal risk model. Rocky Mountain J. Math. 43(4):1395–1414.
   Web of Science ®Google Scholar