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Towards zero variance estimators for rare event probabilities

Abstract : Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events $E_{n}:=\left( u(X_{1})+...+u(X_{n}\right) )\in A_{n}$ where the summands are i.i.d. and $E_{n}$ is a large or moderate deviation event. The approximation of the conditional density of the vector $\left( X_{1},...,X_{k_{n}}\right) $ with respect to $E_{n}$ on long runs, when $% k_{n}/n\rightarrow1$, is handled. The maximal value of $k_{n}$ compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical IS schemes. Detailed algorithms are proposed.
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Contributor : Michel Broniatowski <>
Submitted on : Friday, February 3, 2012 - 4:31:50 PM
Last modification on : Thursday, December 10, 2020 - 11:01:35 AM
Long-term archiving on: : Friday, May 4, 2012 - 2:47:21 AM


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  • HAL Id : hal-00613346, version 2


Michel Broniatowski, Virgile Caron. Towards zero variance estimators for rare event probabilities. ACM Transactions on Modeling and Computer Simulation, Association for Computing Machinery, 2013, 23 (1), pp. 7, 23. ⟨hal-00613346v2⟩



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