Asymptotic behavior of tail and local probabilities for sums of subexponential random variables

Journal of Applied Probability

Volumn 41, Issue 1, 2004, Pages 108-116

  Ng, Kai W ^a   Tang, Qihe ^b  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b UNIVERSITY OF AMSTERDAM   (Netherlands)

Author keywords

Asymptotics; Local probability; Partial sum; Subexponentiality; Tail probability

Indexed keywords

EID: 2442454865     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1077134671     Document Type: Article

References (21)

1. ASMUSSEN, S., Foss, S. AND KORSHUNOV, D. (2003). Asymptotics for sums of random variables with local subexponential behaviour. J. Theoret. Prob. 16, 489-518.
2. ASMUSSEN, S. et al. (2002). A local limit theorem for random walk maxima with heavy tails. Statist. Prob. Lett. 56, 399-404.
3. ATHREYA, K. B. AND NEY, P. E. (1972). Branching Processes. Springer, New York.
4. BERTOIN, J. AND DONEY, R. A. (1994). On the local behaviour of ladder height distributions. J. Appl. Prob. 31, 816-821.
5. BINGHAM, N. H., GOLDIE, C. M. AND TEUGELS, J. L. (1987). Regular Variation. Cambridge University Press.
6. CHISTYAKOV, V. P. (1964). A theorem on the sums of independent positive random variables and its applications to branching random processes. Theory Prob. Appl. 9, 640-648.
7. CHOVER, J., NEY, P. AND WAINGER, S. (1973). Functions of probability measures. J. Anal. Math. 26, 255-302.
8. CLINE, D. B. H. (1994). Intermediate regular and Π variation. Proc. London Math. Soc. 68, 594-616.
9. EMBRECHTS, P. AND OMEY, E. (1984). A property of longtailed distributions. J. Appl. Prob. 21, 80-87.
10. EMBRECHTS, P. AND VERAVERBEKE, N. (1982). Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55-72.
11. EMBRECHTS, P., KLÜPPELBERG, C. AND MIKOSCH, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.
12. Foss, S. AND ZACHARY, S. (2003). The maximum on a random time interval of a random walk with long-tailed increments and negative drift. Ann. Appl. Prob. 13, 37-53.
13. GOLDIE, C. M. (1978). Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440-442.
14. KLÜPPELBERG, C. (1988). Subexponential distributions and integrated tails. J. Appl. Prob. 25, 132-141.
15. KLÜPPELBERG, C. (1989). Subexponential distributions and characterization of related classes. Prob. Theory Relat. Fields 82, 259-269.
16. NG, K. W., TANG, Q. AND YANG, H. (2002). Maxima of sums of heavy-tailed random variables. ASTIN Bull. 32, 43-55.
17. PETROV, V. V. (1975). A generalization of an inequality of Lévy. Theory Prob. Appl. 20, 141-145.
18. SGIBNEV, M. S. (1996). On the distribution of the maxima of partial sums. Statist. Prob. Lett. 28, 235-238.
19. TANG, Q. (2002). An asymptotic relationship for ruin probabilities under heavy-tailed claims. Sci. China A 45, 632-639.
20. TANG, Q. AND YAN, J. (2002). A sharp inequality for the tail probabilities of sums of i.i.d. r.v.'s with dominatedly varying tails. Sci. China A 45, 1006-1011.
21. VERAVERBEKE, N. (1977). Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stoch. Process. Appl. 5, 27-37.