 |
|
|
|
| HAL : hal-00688165, version 3 |
| arXiv : 1204.3730 |
| Fiche détaillée |  Récupérer au format |
|
|
| Versions disponibles : | v1 (17-04-2012) | v2 (27-09-2012) | v3 (11-12-2012) |
|
|
|
|
| Concentration Bounds for Stochastic Approximations |
|
|
| Noufel Frikha 1Stephane Menozzi 2 |
|
|
| (16/04/2012) |
|
|
|
| We obtain non asymptotic concentration bounds for two kinds of stochastic approximations. We first consider the deviations between the expectation of a given function of the Euler scheme of some diffusion process at a fixed deterministic time and its empirical mean obtained by the Monte-Carlo procedure. We then give some estimates concerning the deviation between the value at a given time-step of a stochastic approximation algorithm and its target. Under suitable assumptions both concentration bounds turn out to be Gaussian. The key tool consists in exploiting accurately the concentration properties of the increments of the schemes. For the first case, as opposed to the previous work of Lemaire and Menozzi (EJP, 2010), we do not have any systematic bias in our estimates. Also, no specific non-degeneracy conditions are assumed. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
|
|
|
CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
|
|
| 2 : | Laboratoire d'analyse et probabilités |
|
|
|
Université d'Evry-Val d'Essonne : EA2172 |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Probabilités |
|
|
| Non asymptotic bounds – Euler scheme – Stochastic approximation algorithms – Gaussian concentration |
|
|
|
|
|
| hal-00688165, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00688165 | |
| oai:hal.archives-ouvertes.fr:hal-00688165 | |
| Contributeur : Stephane Menozzi | |
| Soumis le : Lundi 10 Décembre 2012, 14:36:10 | |
| Dernière modification le : Mardi 11 Décembre 2012, 09:59:13 | |
