Importance Sampling and the Cyclic Approach

References

• Asmussen S. Risk theory in a Markovian environment. Scand. Actuarial J. (1989) 69–100Crossref, Google Scholar
• Asmussen S., Binswanger K. Simulation of ruin probabilities for subexponential claims. Astin Bulletin (1997) 27(2):297–318Crossref, Google Scholar
• Avi-Itzhak B., Noar P. Some queueing problems with the service station subject to breakdowns. Oper. Res. (1963) 11:303–320Link, Google Scholar
• Chang C. S., Heidelberger P., Juneja S., Shahabuddin P. Effective bandwidth and fast simulation of ATM intree networks. Performance Evaluation (1994) 20:45–65Crossref, Google Scholar
• Cottrell M., Fort J. C., Malgouyres G. Large deviations and rare events in the study of stochastic algorithms. IEEE Trans. Automatic Control (1983) 28:907–918Crossref, Google Scholar
• Dembo A., Zeitouni O.Large Deviations Techniques and Applications (1992) (Jones and Bartlett, Boston, MA) Google Scholar
• Frater M. R., Bitmead R. R., Kennedy R. A., Anderson B. D. O. Fast simulation of rare events using reverse-time models. North-Holland Computer Networks and ISDN Systems (1990) 20:315–321Crossref, Google Scholar
• Glasserman P., Wang Y. Counterexamples in importance sampling for large deviations probabilities. Ann. Appl. Probab. (1997) 7:731–746Crossref, Google Scholar
• Glynn P. W., Heidelberger P., Nicola V. F., Shahabuddin P. Efficient estimation of steady-state measures in non-regenerative dependability models. Proc. 1993 Winter Simulation Conf. (1993) (IEEE Press)311–316Crossref, Google Scholar
• Golub G. H., Loan C. F. V.Matrix Computations (1996) 3rd Ed.(Johns Hopkins University Press, Baltimore, MD) Google Scholar
• Heidelberger P. Fast simulation of rare events in queueing and reliability models. ACM Trans. on Modeling and Comput. Simulation (1995) 5(1):43–85Crossref, Google Scholar
• Iscoe I., Ney P., Nummelin E. Large deviations of uniformly recurrent Markov additive processes. Adv. Appl. Math. (1985) 6:373–412Crossref, Google Scholar
• Juneja S. Efficient rare event simulation of stochastic systems. (1993) . Ph. D. dissertation, Department of Operations Research, Stanford University, Stanford, CAGoogle Scholar
• Juneja S., Shahabuddin P. Efficient simulation of Markov chains with small transition probabilities. Management Sci. (2001) 47(4):547–562Link, Google Scholar
• Juneja S., Shahabuddin P., Chandra A. Simulating heavy tailed processes using delayed hazard rate twisting. Proc. 1999 Winter Simulation Conf. (1999) (IEEE Press)420–427Crossref, Google Scholar
• Karlin S., Taylor H. M.A First Course in Stochastic Processes (1975) 2nd ed.(Academic Press, New York) Google Scholar
• Kelly F. P.Reversibility and Stochastic Processes (1979) (Wiley, New York) Google Scholar
• Kesidis G., Walrand J. Quick simulation at ATM buffers with on-off multiclass Markov fluid sources. ACM Trans. Model Comput. Simul. (1993) 3:269–276Crossref, Google Scholar
• Lehtonen T., Nyrhinen H. Simulating level-crossing probabilities by importance sampling. Adv. Appl. Probab. (1992a) 24:858–874Crossref, Google Scholar
• Lehtonen T., Nyrhinen H. On asymptotically efficient simulation of ruin probabilities in a Markovian environment. Scand. Actuarial. J. (1992b) 60–75Crossref, Google Scholar
• Meyn S. P., Tweedie R. L. Stability of Markovian processes I: Criteria for discrete time chains. Adv. Appl. Prob. (1992) 24:542–574Crossref, Google Scholar
• Mitrani I. Queues with breakdowns. Second International Workshop on Performability Modelling of Comp. and Comm. Syst. (1993) (Mont St. Michel)Google Scholar
• Parekh S., Walrand J. A quick simulation method for excessive backlogs in networks of queues. IEEE Trans. Automatic Control (1989) 34(1):54–66Crossref, Google Scholar
• Royden H. L.Real Analysis (1987) (Macmillan Publishing Company, New York) Google Scholar
• Sadowsky J. S. Large deviations and efficient simulation of excessive backlogs in a GI/G/m Queue. IEEE Trans. Automatic Control (1991) 36(12):1383–1394Crossref, Google Scholar
• Sadowsky J. S. On Monte Carlo estimation of large deviations probabilities. Ann. of Appl. Probab. (1996) 6(2):399–422Crossref, Google Scholar
• Sadowsky J. S., Szpankowski W. The probability of large queue lengths and waiting times in a heterogeneous multiserver queue part I: Tight limits. Adv. Appl. Prob. (1995) 27:532–566Crossref, Google Scholar
• Shwartz A., Weiss A. Induced rare events: Analysis via large deviations and time reversal. Adv. Appl. Prob. (1993) 25:667–689Crossref, Google Scholar
• Siegmund D. Importance sampling in the Monte Carlo study of sequential tests. Ann. Statist. (1976) 4:673–684Crossref, Google Scholar