Zero-Variance Importance Sampling Estimators for Markov Process Expectations

Published Online:https://doi.org/10.1287/moor.1120.0569

References

  • Ahamed TPI, Borkar VS, Juneja S. Adaptive importance sampling technique for Markov chains using stochastic approximation. Oper. Res. (2006) 54(3):489–504LinkGoogle Scholar
  • Baggerly K, Cox D, Picard R. Exponential convergence of adaptive importance sampling for Markov chains. J. Appl. Probab. (2000) 37(2):342–358CrossrefGoogle Scholar
  • Blanchet J, Glynn P. Efficient rare event simulation for the maximum of heavy-tailed random walks. Ann. Appl. Probab. (2008) 18(4):1351–1378CrossrefGoogle Scholar
  • Bolia N, Juneja S, Glasserman P, Ingalls RG, Rosetti MD, Smith JS, Peters BA. Function-approximation-based importance sampling for pricing American options. Proc. 2004 Winter Simulation Conf. (2004) (IEEE Computer Society, Washington, DC) 604–611Google Scholar
  • Booth TE. Zero-variance solutions for linear Monte-Carlo. Nuclear Sci. Engrg. (1989) 102(4):332–340Google Scholar
  • Borkar VS, Juneja S, Kherani AA. Performance analysis conditioned on rare events: An adaptive simulation scheme. Comm. Inform. Systems (2004) 3(4):259–278CrossrefGoogle Scholar
  • Borodin AN, Salminen P. Handbook of Brownian Motion : Facts and Formulae (2002) 2nd ed.(Birkhäuser, Basel, Boston) CrossrefGoogle Scholar
  • Chang C-S, Heidelberger P, Juneja S, Shahabuddin P. Effective bandwidth and fast simulation of ATM intree networks. Performance Eval. (1994) 20(1):45–66CrossrefGoogle Scholar
  • Chung KL. Markov Chains with Stationary Transition Probabilities (1967) 2nd ed.(Springer, Berlin) Google Scholar
  • Dupuis P, Wang H. Importance sampling, large deviations, and differential games. Stochastic and Stochastics Rep. (2004) 76(6):481–508CrossrefGoogle Scholar
  • Dupuis P, Wang H. Dynamic importance sampling for uniformly recurrent Markov chains. Ann. Appl. Probab. (2005) 15(1A):1–38CrossrefGoogle Scholar
  • Fox BL, Glynn PW. Discrete-time conversion for simulating finite-horizon Markov processes. SIAM J. Appl. Math. (1990) 50(5):1457–1473CrossrefGoogle Scholar
  • Glasserman P. Filtered Monte Carlo. Math. Oper. Res. (1993) 18(3):610–634LinkGoogle Scholar
  • Glasserman P. Monte Carlo Methods in Financial Engineering (2004) (Springer, New York) CrossrefGoogle Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P. Asymptotically optimal importance sampling and stratification for pricing path-dependent options. Math. Finance (1999) 9(2):117–152CrossrefGoogle Scholar
  • Glynn PW, Iglehart DL. Importance sampling for stochastic simulations. Management Sci. (1989) 35(11):1367–1392LinkGoogle Scholar
  • Glynn PW, Heidelberger P, Nicola VF, Shahabuddin P, Evans GW, Mollaghasemi M, Russell EC, Biles WE. Efficient estimation of the mean time between failures in non-regenerative dependability models. Proc. 1993 Winter Simulation Conf. (1993) (IEEE Computer Society, Washington, DC) 361–366Google Scholar
  • Goyal A, Shahabuddin P, Heidelberger P, Nicola VF, Glynn PW. A unified framework for simulating Markovian models of highly dependable systems. IEEE Trans. Comput. (1992) 41(1):36–51CrossrefGoogle Scholar
  • Halton JH. Sequential Monte Carlo. Proc. Cambridge Philos. Soc. (1962) 58:57–78CrossrefGoogle Scholar
  • Hammersley JM, Handscomb DC. Monte Carlo Methods (1964) (Methuen, London) Methuen's Monographs on Applied Probability and StatisticsCrossrefGoogle Scholar
  • Harrison JM. Brownian Motion and Stochastic Flow Systems (1985) (Wiley, New York) Google Scholar
  • Heidelberger P. Fast simulation of rare events in queueing and reliability models. ACM Trans. Modeling Comput. Simulation (1995) 5(1):43–85CrossrefGoogle Scholar
  • Heidelberger P, Shahabuddin P, Nicola VF. Bounded relative error in estimating transient measures of highly dependable non-Markovian systems. ACM Trans. Modeling Comput. Simulation (1994) 4(2):137–164CrossrefGoogle Scholar
  • Henderson SG, Glynn PW. Approximating martingales for variance reduction in Markov process simulation. Math. Oper. Res. (2002) 27(2):253–271LinkGoogle Scholar
  • Karatzas I, Shreve S. Brownian Motion and Stochastic Calculus (1991) 2nd ed.(Springer-Verlag, New York) Google Scholar
  • Kollman C, Baggerly K, Cox D, Picard R. Adaptive importance sampling on discrete Markov chains. Ann. Appl. Probab. (1999) 9(2):391–412CrossrefGoogle Scholar
  • L'Ecuyer P, Tuffin B, Mason SJ, Hill RR, Mönch L, Rose O, Jefferson T, Fowler JW. Approximate zero-variance simulation.. Proc. 2008 Winter Simulation Conf. (2008) (IEEE Computer Society, Washington, DC) 170–181CrossrefGoogle Scholar
  • Meyn S, Tweedie RL. Markov Chains and Stochastic Stability (2009) 2nd ed.(Cambridge University Press, New York) CrossrefGoogle Scholar
  • Nakayama MK. General conditions for bounded relative error in simulations of highly reliable Markovian systems. Adv. Appl. Probab. (1996) 28(3):687–727CrossrefGoogle Scholar
  • Øksendal B. Stochastic Differential Equations: An Introduction with Applications (2000) 5th ed.(Springer, Berlin) Google Scholar
  • Sadowsky JS. Large deviations theory and efficient simulation of excessive backlogs in a GI/GI/m queue. IEEE Trans. Automatic Control (1991) 36(12):1383–1394CrossrefGoogle Scholar
  • Salminen P, Norros I. On busy periods of the unbounded Brownian storage. Queueing Systems (2001) 39(4):317–333CrossrefGoogle Scholar
  • Shahabuddin P. Importance sampling for the simulation of highly reliable Markovian systems. Management Sci. (1994) 40(3):333–352LinkGoogle Scholar
  • Smith PJ, Shafi M, Gao H. Quick simulation: A review of importance sampling techniques in communications systems. IEEE J. Selected Areas Comm. (1997) 15(4):597–613CrossrefGoogle Scholar
  • Su Y, Fu MC, Joines JA, Barton RR, Kang K, Fishwick PA. Importance sampling in derivative securities pricing. Proc. 2000 Winter Simulation Conf. (2000) (IEEE Computer Society, Washington, DC) 587–596CrossrefGoogle Scholar
  • Whitt W. Stochastic-Process Limits: An Introduction to Stochastic-Process Limits and Their Application to Queues (2002) (Springer-Verlag, New York) Springer Series in Operations ResearchCrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.