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On asymptotically efficient simulation of large deviation probabilities

Part of: Special processes Limit theorems Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 July 2016

A. B. Dieker  and
M. Mandjes
A. B. Dieker*
Affiliation:
CWI and University of Twente
M. Mandjes*
Affiliation:
CWI and University of Amsterdam
*
∗ Postal address: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
∗ Postal address: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.
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Abstract

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Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable set A and some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

Keywords

Asymptotic efficiencyimportance samplinglarge deviation

MSC classification

Primary: 65C05: Monte Carlo methods
Secondary: 60F10: Large deviations 60K10: Applications (reliability, demand theory, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 2 , June 2005 , pp. 539 - 552
Copyright
Copyright © Applied Probability Trust 2005 

Footnotes

Supported by the Netherlands Organization for Scientific Research (NWO) under grant 631.000.002.

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