Approximate zero-variance simulation

Proceedings - Winter Simulation Conference

Volumn , Issue , 2008, Pages 170-181

  L'Ecuyer, Pierre ^a   Tuffin, Bruno ^b  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE VERSIONS; APPROXIMATE ZEROS; CENTRAL LIMIT THEOREMS; COMPUTATIONAL EFFORTS; CONVERGENCE RATES; EFFICIENCY GAINS; ESTIMATION ERRORS; ESTIMATION PROBLEMS; EXPONENTIAL CONVERGENCES; FASTER CONVERGENCES; MONTE CARLO SIMULATIONS; RARE-EVENT SIMULATIONS; SQUARE ROOTS; VARIANCE REDUCTION TECHNIQUES; ZERO VARIANCES;

MONTE CARLO METHODS;

ESTIMATION;

EID: 60749118344     PISSN: 08917736     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/WSC.2008.4736066     Document Type: Conference Paper

References (40)

1. Ahamed, I" V, S. Borkar, and S, Juneja, 2006. Adaptive importance sampling for Markov chains using stochastic approximation. Operations Research 54 (3): 489-504.
2. Asmussen, S., and P. W. Glynn. 2007. Stochastic simulation. New York: Springer-Verlag.
3. Baggerly, K., D. Cox, and R. Picard. 2000. Exponential convergence of adaptive importance sampling for Markov chains. Journal of Applied Probability 37 (2): 342-358.
4. Ben-Ameur, H., P. L'Ecuyer, and C. Lemieux. 2004. Combination of general antithetic transformations and control variables. Mathematics of Operations Research 29 (4): 946-960.
5. Blanchet, J" and P. W. Glynn. 2007. Efficient rare-event simulation for the maximum of a random walk with heavy-tailed increments. Manuscript.
6. Bolia, N., S. Juneja, and P. Glasserman. 2004. Functionapproximation- based importance sampling for pricing American options. In Proceedings of the 2004 Winter Simulation Conference, 604-611. Pistacaway, NJ: IEEE Press.
7. Booth, T. E. 1985. Exponential convergence for Monte Carlo particle transport? Transactions of the American Nuclear Society 50:267-268.
8. Booth, T. E. 1987. Generalized zero-variance solutions and intelligent random numbers. In Proceedings of the 1987 Winter Simulation Conference, 445-451: IEEE Press.
9. De Boer, P. T., P. LΈcuyer, G. Rubino, and B. Tuffin. 2007. Estimating the probability of a rare event over a finite horizon. In Proceedings of the 2007 Winter Simulation Conference, 403-111: IEEE Press.
10. Desai, P. Y., and P. W. Glynn. 2001. A Markov chain perspective on adaptive Monte Carlo algorithms. In Proceedings of (he 2001 Winter Simulation Conference, 379-384: IEEE Press.
11. Dick, J. 2008. Explicit constructions of quasi-Monte Carlo rules for the numerical integration of high-dimensional periodic functions. Manuscript, Sydney, Australia.
12. Dick, J., I. H. Sloan, X. Wang, and H. Wozniakowski. 2004. Liberating the weights. Journal of Complexity 20 (5): 593-623.
13. Dick, J., 1. H. Sloan, X. Wang, and H. Wozniakowski. 2006. Good lattice rules in weighted Korobov spaces with general weights. Numerische Mathematik 103:63-97.
14. Dupuis, P., and H. Wang. 2004. Importance sampling, large deviations, and differential games. Stochastics and Stochastics Reports 76:481-508.
15. Fishman, G. S. 1996. Monte Carlo: Concepts, algorithms, and applications. Springer Series in Operations Research. New York, NY: Springer-Verlag.
16. Glasserman, P. 2004. Monte Carlo methods in financial engineering. New York: Springer-Verlag.
17. Glynn, P. W., and W. Whitt. 1992. The asymptotic efficiency of simulation estimators. Operations Research 40:505-520.
18. Heidelberger, P. 1995. Fast simulation of rare events in queueing and reliability models. ACM Transactions on Modeling and Computer Simulation 5 (1): 43-85.
19. Henderson, S. G., and P. W. Glynn. 2002. Approximating martingales for variance reduction in Markov process simulation. Mathematics of Operations Research 27:253-271.
20. Henderson, S. G., and B. Simon. 2004. Adaptive simulation using perfect control variates. Journal of Applied Probability 41:859-876.
21. Hickernell, F. J. 2003. My dream quadrature rule. Journal of Complexity 19:420-27.
22. Juneja, S., and P. Shahabuddin. 2006. Rare event simulation techniques: An introduction and recent advances. In Simulation, ed. S. G. Henderson and B. L. Nelson, Handbooks in Operations Research and Management Science, 291-350. Amsterdam, The Netherlands: Elsevier. Chapter 11.
23. Kim, S., and S. G. Henderson. 2006. Adaptive control variates for finite-horizon simulation. Mathematics of Operations Research 32:508-527.
24. Kim, S., and S. G. Henderson. 2007. Non-linear control variates for regenerative steady-state simulation. In Proceedings of the 2007 Winter Simulation Conference, 430-438: IEEE Press.
25. Kollman, C, K. Baggerly, D. Cox, and R. Picard. 1999. Adaptive importance sampling on discrete Markov chains. Annals of Applied Probability 9 (2): 391-412.
26. Kuruganti, 1., and S. Strickland. 1996. Importance sampling for Markov Chains: computing variance and determining optimal measures. In Proceedings of the 1996 Winter Simulation Conference, 273-280: IEEE Press.
27. L'Ecuyer, P. 2008. Quasi-Monte Carlo methods with applications in finance. Finance and Stochastics. To appear.
28. LΈcuyer, P., J. H. Blanchet, B. Tuffin, and P. W. Glynn. 2008. Asymptotic robustness of estimators in rare-event simulation. ACM Transactions on Modeling and Computer Simulation. To appear.
29. LΈcuyer, P., C. Lécot, and B. Tuffin. 2008. A randomized quasi-Monte Carlo simulation method for Markov chains. Operations Research. To appear.
30. L'Ecuyer, P., and C. Lemieux. 2000. Variance reduction via lattice rules. Management Science 46 (9): 1214-1235.
31. LΈcuyer, P., and C. Lemieux. 2002. Recent advances in randomized quasi-Monte Carlo methods. In Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, ed. M. Dror, P. LΈcuyer, and F. Szidarovszky, 419-474. Boston: Kluwer Academic.
32. LΈcuyer, P., and B. Tuffin. 2007. Effective approximation of zero-variance simulation in a reliability setting. In Proceedings of the 2007 European Simulation and Modeling Conference, 48-54. Ghent, Belgium: EUROS1S.
33. Nakayama, M. K. 1996. General conditions for bounded relative error in simulations of highly reliable Markovian systems. Advances in Applied Probability 28:687-727.
34. Niederreiter, H. 1992. Random number generation and quasi-Monte Carlo methods, Volume 63 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia, PA: SIAM.
35. Owen, A. B. 2003. Variance with alternative scramblings of digital nets. ACM Transactions on Modeling and Computer Simulation 13 (4): 363-378.
36. Rubinstein, R. Y. 1999. The cross-entropy method for combinatorial and continuous optimization. Methodology and Computing in Applied Probability 2:127-190.
37. Rubinstein, R. Y, and A. Shapiro. 1993. Discrete event systems: Sensitivity analysis and stochastic optimization by the score function method. New York: Wiley.
38. Shahabuddin, P. 1994. Importance sampling for the simulation of highly reliable Markovian systems. Management Science 40 (3): 333-352.
39. Sloan, I. H., and S. Joe. 1994. Lattice methods for multiple integration. Oxford: Clarendon Press.
40. Wilson, J. R. 1979. Proof of the antithetic-variates theorem for unbounded functions. Math. Proc. Camb. Phil. Soc. 86:477-479.