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May 1996 On Monte Carlo estimation of large deviations probabilities
John S. Sadowsky
Ann. Appl. Probab. 6(2): 399-422 (May 1996). DOI: 10.1214/aoap/1034968137


Importance sampling is a Monte Carlo technique where random data are sampled from an alternative "sampling distribution" and an unbiased estimator is obtained by likelihood ratio weighting. Here we consider estimation of large deviations probabilities via importance sampling. Previous works have shown, for certain special cases, that "exponentially twisted" distributions possess a strong asymptotic optimality property as a sampling distribution. The results of this paper unify and generalize the previous special case results. The analysis is presented in an abstract setting, so the results are quite general and directly applicable to a number of large deviations problems. Our main motivation, however, is to attack sample path problems. To illustrate the application to this class of problems, we consider Mogulskii type sample path problems in some detail.


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John S. Sadowsky. "On Monte Carlo estimation of large deviations probabilities." Ann. Appl. Probab. 6 (2) 399 - 422, May 1996.


Published: May 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0855.60031
MathSciNet: MR1398051
Digital Object Identifier: 10.1214/aoap/1034968137

Primary: 60F10 , 65C05
Secondary: 93E30

Keywords: computer simulations of stochastic systems , large deviations , Monte Carlo methods

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 2 • May 1996
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