State-dependent importance sampling for regularly varying random walks

Advances in Applied Probability

Volumn 40, Issue 4, 2008, Pages 1104-1128

  Blanchet, Jose H ^a   Liu, Jingchen ^b  

^a Columbia University ^*  (United States)

^b Och Spine at New York Presbyterian Hospitals   (United States)

Author keywords

Heavy tail; Importance sampling; Random walk; Rare event simulation; Regularly varying; State dependent; Strong efficiency

Indexed keywords

ALGORITHMS; ELECTRIC NETWORK ANALYSIS; ESTIMATION; LEARNING ALGORITHMS; MIXTURES; RANDOM VARIABLES; TELECOMMUNICATION NETWORKS;

HEAVY TAIL; IMPORTANCE SAMPLING; RANDOM WALK; RARE-EVENT SIMULATION; REGULARLY VARYING; STATE DEPENDENT; STRONG EFFICIENCY;

APPROXIMATION ALGORITHMS;

EID: 59549101238     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1231340166     Document Type: Article

References (34)

1. ADLER, J., FELDMAN, R. AND TAQQU, M. (eds) (1998). A Practical Guide to Heavy Tails: Statistical Techniques and Applications. Birkhäuser, Boston, MA.
2. ANANTHARAM, V. (1989). How large delays build up in a GI/GI/I queue. Queueing Systems 5, 345-367.
3. ASMUSSEN, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.
4. ASMUSSEN, S. AND GLYNN, P. (2007). Stochastic Simulation: Algorithms and Analysis. Springer, New York.
5. ASMUSSEN, S. AND KROESE, D. P. (2006). Improved algorithms for rare event simulation with heavy tails. Adv. Appl. Prob. 38, 545-558.
6. ASMUSSEN, S., BINSWANGER, K. AND HØJGAARD, B. (2000). Rare event simulation for heavy-tailed distributions. Bernoulli 6, 303-322.
7. BASSAMBOO, A., JUNEJA, S. AND ZEEVI, A. (2005). Importance sampling simulation in the presence of heavy tails. In Proc. 37th Conf. Winter Simulation (December 2005), IEEE, pp. 664-672.
8. BLANCHET, J. AND GLYNN, P. (2008). Efficient rare-event simulation for the maximum of heavy-tailed random walks. Ann. Appl. Prob. 18, 1351-1378.
9. BLANCHET, J. AND LIU, J. C. (2006). Efficient simulation for large deviation probabilities of sums of heavy-tailed increments. In Proc. 38th Conf. Winter Simulation (December 2006), IEEE, pp. 757-764.
10. BLANCHET, J. AND LIU, J. C. (2007). Path-sampling for state-dependent importance sampling. In Proc. 39th Conf. Winter Simulation (December 2007), IEEE, pp. 380-388.
11. BLANCHET, J., GLYNN, P. AND LIU, J. C. (2007). Fluid heuristics, Lyapunov bounds and efficient importance sampling for a heavy-tailed G/G/ 1 queue. Queueing Systems 57, 99-113.
12. BLANCHET, J., GLYNN, P. AND LIU, J. C. (2008). Efficient rare event simulation for heavy-taded multiserver queues. Department of Statistics, Columbia University.
13. BOROVKOV, A. A. AND BOROVKOV, K. A. (2001). On large deviations of probabilities for random walks. I. Regularly varying distribution tails. Theory Prob. Appl. 49, 193-213.
14. BUCKLEW, J. (2004). Introduction to Rare Event Simulation. Springer, New York.
15. DEMBO, A. AND ZEITOUNI O. (1998). Large Deviations Techniques and Applications, 2nd edn. Springer, New York.
16. DONSKFR, M. AND VARADHAN, S. (1975). Asymptotic evaluation ofcertain Markov process expectations for large time. I. II. Commun. Pure Appl. Math. 28, 1-47.
17. DUPUIS, P. AND WANG, H. (2004). Importance sampling, large deviations, and differential games. Stoch. Stach. Reports 76, 481-508.
18. DUPUIS, P. AND WANG, H. (2005). On the convergence from discrete to continuous time in an optimal stopping problem. Ann. Appl. Prob. 15, 1339-1366.
19. DUPUIS, P., LEDER, K. AND WANG, H. (2007). Importance sampling for sums of random variables with regularly varying tails. ACM Trans. Model. Comput. Simul. 17, 1-21.
20. FOSS, S. AND KORSHUNOV, D. (2006). Heavy tails in multi-server queues. Queueing Systems 52, 31-48.
21. FOSS, S., KONSTANTOPOULOS, T. AND ZACHARY, S. (2007). Discrete and continuous time modulated random walks with heavy-tailed increments. J Theoret. Prob. 20, 581-612.
22. GLASSERMAN, P. (2004). Monte Carlo Methods in Financial Engineering (Appl. Math. 53). Springer. New York.
23. GLASSERMAN, P. AND KOU, S. (1995). Analysis of an importance sampling estimator for tandem queues. ACM Trans. Model. Comput. Simul. 4, 22-42.
24. GLASSERMAN, P. AND WANG, Y. (1997). Counterexamples in importance sampling for large deviations probabilities. Ann. Appl. Prob. 7, 731-746.
25. HULT, H. AND LINDSKOG, F. (2005). Extremal behavior for regularly varying stochastic processes. Stoch. Process. Appl. 115, 249-274.
26. HULT, H., LINDSKOG, F., MIKOSCH, T. AND SAMORODNITSKY, G. (2005). Functional large deviations for multivariate regularly random walks. Ann. Appl. Prob. 15, 2651-2680.
27. JUNEJA, S. AND SHAHABUDDIN, P. (2002). Simulating heavy tailed processes using delayed hazard rate twisting. ACM Trans. Model. Comput. Simul. 12, 94-118.
28. JUNEJA, S. AND SHAHABUDDIN, P. (2006). Rare event simulation techniques: introduction and recent advances. In Handbook on Simulation, eds S. Henderson and B. Nelson, North-Holland, Amsterdam, pp. 291-350.
29. NAGAEV, A. V. (1969a). Integral limit theorems for large deviations when Cramér's condition is not fulfilled. I. Theory Prob. Appl. 14, 51-64.
30. NAGAEV, A. V. (1969b). Integral limit theorems for large deviations when Cramér's condition is not satisfied. II. Theory Prob. Appl. 14, 193-208.
31. RESNICK, S. (1987). Extreme Values, Regular Variation, and Point Processes (Appl. Prob. 4). Springer, New York.
32. ROZOVSKII, L. V. (1989). Probabilities of large deviations of sums of independent random variables with common distribution function in the domain of attraction of the normal law. Theory Prob. Appl. 34, 625-644.
33. SADOWSKY, J. S. AND BUCKLEW, J. (1990), On large deviations theory and asymptotically efficient Monte Carlo estimation. IEEE Trans. Inf. Theory 36, 579-588.
34. ZWART, A. (2001). Queueing systems with heavy tails. Doctoral Thesis, Technische Universiteit Eindhoven.