Using Poisson processes for rare event simulation

Abstract : This thesis address the issue of extreme event simulation. From a original understanding of the Splitting methods, a new theoretical framework is proposed, regardless of any algorithm. This framework is based on a point process associated with any real-valued random variable and lets defined probability, quantile and moment estimators without any hypothesis on this random variable. The artificial selection of threshold in Splitting vanishes and the estimator of the probability of exceeding a threshold is indeed an estimator of the whole cumulative distribution function until the given threshold. These estimators are based on the simulation of iid. replicas of the point process. So they allow for the use of massively parallel computer cluster. Suitable practical algorithms are thus proposed. Finally it can happen that these advanced statistics still require too much samples. In this context the computer code is considered as a random process with known distribution. The point process framework lets handle this additional source of uncertainty and estimate easily the conditional expectation and variance of the resulting random variable. It also defines new SUR enrichment criteria designed for extreme event probability estimation.
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Submitted on : Saturday, August 19, 2017 - 9:21:34 PM
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  • HAL Id : tel-01575418, version 1

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Clément Walter. Using Poisson processes for rare event simulation. Computation [stat.CO]. Université Paris Diderot / Sorbonne Paris Cité, 2016. English. ⟨tel-01575418⟩

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