# Limit theorems for weighted and regular Multilevel estimators

Abstract : We aim at analyzing in terms of a.s. convergence and weak rate the performances of the Multilevel Monte Carlo estimator (MLMC) introduced in [Gil08] and of its weighted version, the Multilevel Richardson Romberg estimator (ML2R), introduced in [LP14]. These two estimators permit to compute a very accurate approximation of $I_0 = \mathbb{E}[Y_0]$ by a Monte Carlo type estimator when the (non-degenerate) random variable $Y_0 \in L^2(\mathbb{P})$ cannot be simulated (exactly) at a reasonable computational cost whereas a family of simulatable approximations $(Y_h)_{h \in \mathcal{H}}$ is available. We will carry out these investigations in an abstract framework before applying our results, mainly a Strong Law of Large Numbers and a Central Limit Theorem, to some typical fields of applications: discretization schemes of diffusions and nested Monte Carlo.
Keywords :
Type de document :
Article dans une revue
Monte Carlo Methods and Applications, De Gruyter, 2017, 23 (1), pp.43. 〈https://www.degruyter.com/〉. 〈10.1515/mcma-2017-0102〉
Domaine :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01398292
Contributeur : Vincent Lemaire <>
Soumis le : jeudi 17 novembre 2016 - 09:01:47
Dernière modification le : vendredi 4 janvier 2019 - 17:32:34

### Citation

Daphné Giorgi, Vincent Lemaire, Gilles Pagès. Limit theorems for weighted and regular Multilevel estimators. Monte Carlo Methods and Applications, De Gruyter, 2017, 23 (1), pp.43. 〈https://www.degruyter.com/〉. 〈10.1515/mcma-2017-0102〉. 〈hal-01398292〉

### Métriques

Consultations de la notice