Counterexamples in importance sampling for large deviations probabilities

Annals of Applied Probability

Volumn 7, Issue 3, 1997, Pages 731-746

  Glasserman, Paul ^a   Wang, Yashan ^a  

^a Columbia University ^*  (United States)

Author keywords

Importance sampling; Large deviations; Monte Carlo methods; Random walks; Rare events; Simulation

Indexed keywords

EID: 0031481011     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034801251     Document Type: Article

References (31)

1. ANANTHARAM, V., HEIDELBERGER, P. and TSOUCAS, P. (1990). Analysis of rare events in continuous time Markov chains via time reversal and fluid approximations. Research Report RC-16280, IBM, Yorktown Heights, NY.
2. ASMUSSEN, S. (1982). Conditioned limit theorems relating a random walk to its associate. Adv. in Appl. Probab. 14 143-170.
3. ASMUSSEN, S. (1985). Conjugate processes and the simulation of ruin probabilities. Stochastic Process. Appl. 20 213-229.
4. ASMUSSEN, S. (1987). Applied Probability and Queues. Wiley, Chichester.
5. ASMUSSEN, S. and BINSWANGER, K. (1995). Simulation of ruin probabilities for subexponential claims. Working paper, Dept. Mathematical Statistics, Univ. Lund, Sweden.
6. ASMUSSEN, S., RUBINSTEIN, R. and WANG, C. L. (1994). Regenerative rare event simulation via likelihood ratios. J. Appl. Probab. 31 797-815.
7. BAZARAA, M. S. and SHETTY, C. M. (1979). Nonlinear Programming: Theory and Algorithms. Wiley, New York.
8. BUCKLEW, J. A. (1990). Large Deviation Techniques in Decision, Simulation, and Estimation. Wiley, New York.
9. BUCKLEW, J. A., NEY, P. and SADOWSKY, J. S. (1990). Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains. J. Appl. Probab. 27 44-59.
10. CHANG, C. S., HEIDELBERGER, P., JUNEJA, P. and SHAHABUDDIN, P. (1994). Effective band-width and fast simulation of ATM intree networks. Performance Evaluation 20 45-65.
11. CHANG, C. S., HEIDELBERGER, P. and SHAHABUDDIN, P. (1995). Fast simulation of packet loss rates in a shared buffer communications switch. ACM Trans. Modeling Comp. Simulation 5 306-325.
12. CHEN, J.-C., LU, D., SADOWSKY, J. S. and YAO, K. (1993). On importance sampling in digital communications. I: fundamentals. IEEE J. Selected Areas in Comm. 11 289-307.
13. DEMBO, A. and ZEITOUNI, O. (1993). Large Deviations Techniques and Applications. Jones and Bartlett, Boston.
14. FRATER, M., LENNON, T. M. and ANDERSON, B. D. O. (1991). Optimally efficient estimation of the statistics of rare events in queuing networks. IEEE Trans. Automat. Control 36 1395-1405.
15. FRESNEDO, R. D. (1989). Quick simulation of rare events in networks. In Proceedings of the Winter Simulation Conference 514-523. Society for Computer Simulation, San Diego.
16. GLASSERMAN, P. and KOU, S. (1995). Analysis of an importance sampling estimator for tandem queues. ACM Trans. Modeling Comp. Simulation 4 22-42.
17. GLYNN, P. W. (1995). Large deviations for the infinite server queue in heavy traffic. IMA Vol. Math. Appl. 71 387-394.
18. HEIDELBERGER, P. (1995). Fast simulation of rare events in queueing and reliability models. ACM Trans. Modeling Comp. Simulation 4 43-85.
19. HEIDELBERGER, P., SHAHABUDDIN, P. and NICOLA, V. (1994). Bounded relative error in estimating transient measures of highly dependable non-Markovian systems. ACM Trans. Modeling Comp. Simulation 4 137-164.
20. KESIDIS, G. and WALRAND, J. (1993). Quick simulation of ATM buffers with on-off multiclass Markov fluid sources. ACM Trans. Modeling Comp. Simulation 3 269-276.
21. LEHTONEN, T. and NYRHINEN, H. (1992). Simulating level-crossing probabilities by importance sampling. Adv. in Appl. Prob. 24 858-874.
22. MCDONALD, D. R. (1995). Asymptotics of first passage times for random walk in a quadrant. Working paper, Dept. Mathematics and Statistics, Univ. Ottawa.
23. NAKAYAMA, M. K. (1994). A characterization of the simple failure biasing method for simulations of highly reliable Markovian systems. ACM Trans. Modeling Comp. Simulation 4 52-88.
24. PAREKH, S. and WALRAND, J. (1989). A quick simulation method for excessive backlogs in networks of queues. IEEE Trans. Automat. Control 34 54-66.
25. SADOWSKY, J. S. (1991). Large deviations and efficient simulation of excessive backlogs in a GI/G/m queue. IEEE Trans. Automat. Control 36 1383-1394.
26. SADOWSKY, J. S. (1993). On the optimality and stability of exponential twisting in Monte Carlo estimation. IEEE Trans. Inform. Theory 39 119-128.
27. SADOWSKY, J. S. (1997). On Monte Carlo estimation of large deviations probabilities. Unpublished manuscript.
28. SADOWSKY, J. S. and BUCKLEW, J. A. (1990). On large deviations theory and asymptotically efficient Monte Carlo estimation. IEEE Trans. Inform. Theory 36 579-588.
29. SHAHABUDDIN, P. (1994). Importance sampling for the simulation of highly reliable Markovian systems. Management Science 40 333-352.
30. SIEGMUND, D. (1976). Importance sampling in the Monte Carlo study of sequential tests. Ann. Statist. 4 673-684.
31. SIEGMUND, D. (1985). Sequential Analysis. Springer, New York.