# Analyse des modeles de branchement avec duplication des trajectoires pour l'étude des événements rares

Abstract : This thesis deals with the splitting method first introduced in rare event analysis in order to speed-up simulation. In this technique, the sample paths are split into $R$ multiple copies at various stages during the simulation. Given the cost, the optimization of the algorithm suggests to take the transition probabilities between stages
equal to some constant and to resample the inverse of that constant subtrials, which may be non-integer and even
unknown but estimated. First, we study the sensitivity of the relative error between the probability of interest $\mathbb{P}(A)$ and its estimator depending on the strategy that makes the resampling numbers integers. Then, since in practice the transition probabilities are generally unknown (and so the optimal resampling umbers), we propose a two-steps algorithm to face that problem. Several numerical applications and comparisons with other models are proposed.
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Cited literature [61 references]

https://tel.archives-ouvertes.fr/tel-00129752
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Submitted on : Thursday, February 8, 2007 - 4:18:32 PM
Last modification on : Monday, July 4, 2022 - 10:22:40 AM
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• HAL Id : tel-00129752, version 1

### Citation

Agnes Lagnoux. Analyse des modeles de branchement avec duplication des trajectoires pour l'étude des événements rares. Mathématiques [math]. Université Paul Sabatier - Toulouse III, 2006. Français. ⟨tel-00129752⟩

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