The overshoot of a random walk with negative drift

Statistics and Probability Letters

Volumn 77, Issue 2, 2007, Pages 158-165

  Tang, Qihe ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

Asymptotics; Ladder height; Tail probabilities; The class S ( ); Uniformity; Wiener Hopf type factorization

Indexed keywords

EID: 33750999331     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2006.06.005     Document Type: Article

References (15)

1. Asmussen S., and Klüppelberg C. Large deviations results for subexponential tails, with applications to insurance risk. Stochastic Process. Appl. 64 1 (1996) 103-125
2. Bingham N.H., Goldie C.M., and Teugels J.L. Regular Variation (1987), Cambridge University Press, Cambridge
3. Chang J.T. Inequalities for the overshoot. Ann. Appl. Probab. 4 4 (1994) 1223-1233
4. Feller, W., 1971. An Introduction to Probability Theory and its Applications, vol. II, second ed. Wiley, New York, London, Sydney.
5. Janson S. Moments for first-passage and last-exit times, the minimum, and related quantities for random walks with positive drift. Adv. in Appl. Probab. 18 4 (1986) 865-879
6. Klüppelberg C. Subexponential distributions and characterizations of related classes. Probab. Theory Related Fields 82 2 (1989) 259-269
7. Klüppelberg C., Kyprianou A.E., and Maller R.A. Ruin probabilities and overshoots for general Lévy insurance risk processes. Ann. Appl. Probab. 14 4 (2004) 1766-1801
8. Pakes A.G. Convolution equivalence and infinite divisibility. J. Appl. Probab. 41 2 (2004) 407-424
9. Rogozin B.A. On the constant in the definition of subexponential distributions. Theory Probab. Appl. 44 2 (2000) 409-412 Translated from Rogozin, B.A., 1999. Teor. Veroyatnost. i Primenen. 44(2), 455-458 (in Russian).
10. Rogozin B.A., and Sgibnev M.S. Banach algebras of measures on the line with given asymptotics of distributions at infinity. Siberian Math. J. 40 3 (1999) 565-576 Translated from Rogozin, B.A., Sgibnev, M.S., 1999. Sibirsk. Mat. Zh. 40(3), 660-672 (in Russian)
11. Shimura T., and Watanabe T. Infinite divisibility and generalized subexponentiality. Bernoulli 11 3 (2005) 445-469
12. Su, C., Chen, J., Hu, Z., 2004. Some discussions on the class L (γ). J. Math. Sci. 122 (4), 3416-3425.
13. Tang Q. A note on the severity of ruin in the renewal model with claims of dominated variation. Bull. Korean Math. Soc. 40 4 (2003) 663-669
14. Tang Q. On convolution equivalence with applications. Bernoulli 12 3 (2006) 535-549
15. Veraverbeke N. Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stochastic Processes Appl. 5 1 (1977) 27-37