Tail asymptotics for the maximum of perturbed random walk

Annals of Applied Probability

Volumn 16, Issue 3, 2006, Pages 1411-1431

  Araman, Victor F ^a,c   Glynn, Peter W ^b,d  

^a NEW YORK UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c NEW YORK UNIVERSITY   (United States)

^d Stanford University   (United States)

Author keywords

Coupling; Cram r Lundberg approximation; Heavy tails; Perturbed random walk; Tail asymptotics

Indexed keywords

EID: 33750506064     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051606000000268     Document Type: Article

References (20)

1. ARAMAN, V. F. (2002). The maximum of perturbed random walk: Limit theorems and applications. Ph.D. dissertation, Management Science and Engineering, Stanford Univ.
2. ARAMAN, V. F. and GLYNN, P. W. (2005). Heavy-traffic diffusion approximations for the maximum of a perturbed random walk. Adv. in Appl. Probab. 37 663-680. MR2156554
3. ASMUSSEN, S. (2003). Applied Probability and Queues, 2nd ed. Springer, New York. MR 1978607
4. BUCKLEW, J. A. (1990). Large Deviation Techniques in Decision, Simulation, and Estimation. Wiley, New York. MR1067716
5. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes Characterization and Convergence. Wiley, New York. MR0838085
6. FELLER, W. (1971). An Introduction to Probability Theory and Its Applications 2, 2nd ed. Wiley, New York. MR0270403
7. GERBER, H. U. (1970). An extension of the renewal theorem and Its application in the collective theory of risk. Skand. Aktuarietidskr. 205-210. MR0353483
8. GLASSERMAN, P. (1997). Bounds and asymptotics for planning critical safety stocks. Oper. Res. 45 244-257.
9. GLASSERMAN, P. and Liu, T. (1997). Corrected diffusion approximations for a multistage production-inventory system. Math. Oper. Res. 22 186-201. MR1436579
10. GUT, A. (1992). First-passage times for perturbed random walks. Sequential Anal. 11149-179. MR1172738
11. KAPLAN, R. (1970). A dynamic inventory model with stochastic lead times. Management Sci. 16491-507.
12. LAI, T. L. and SIEGMUND, D. (1977). A nonlinear renewal theory with applications to sequential analysis. I. Ann. Statist. 5 946-954. MR0445599
13. LAI, T. L. and SIEGMUND, D. (1979). A nonlinear renewal theory with applications to sequential analysis. II. Ann. Statist. 7 60-76. MR0515684
14. NEY, P. (1981). A refinement of the coupling method in renewal theory. Stochastic Process. Appl. 11 11-26. MR0608004
15. SAHIN, I. (1983). On the continuous-review (s, S) inventory model under compound renewal demand and random lead times. J. Appl. Probab. 20 213-219. MR0688099
16. SCHLEGEL, S. (1998). Ruin probabilities in perturbed risk models. Insurance Math. Econom. 2293-104. MR1625799
17. SCHMIDLI, H. (1995). Cramer-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion. Insurance Math. Econom. 16 135-149. MR 1347857
18. THORISSON, H. (2000). Coupling, Stationarity and Regeneration. Springer, New York. MR1741181
19. WOODROOFE, M. (1982). Nonlinear Renewal Theory. SIAM, Philadelphia. MR0660065
20. ZIPKIN, P. (1986). Stochastic leadtimes in continuous time inventory models. Naval Res. Logist. Quart. 33 763-774. MR0860745