Skip to Main content Skip to Navigation
Journal articles

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.
Document type :
Journal articles
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-01398292
Contributor : Vincent Lemaire <>
Submitted on : Thursday, November 17, 2016 - 9:01:47 AM
Last modification on : Saturday, March 28, 2020 - 2:09:42 AM

Links full text

Identifiers

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. ⟨10.1515/mcma-2017-0102⟩. ⟨hal-01398292⟩

Share

Metrics

Record views

436