# 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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Journal articles
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https://hal.sorbonne-universite.fr/hal-00613346
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

### Citation

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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