Probabilités/Statistique
Algorithmes stochastiques à bruit dépendant
[Dependent noise for stochastic algorithms]
Comptes Rendus. Mathématique, Volume 337 (2003) no. 7, pp. 473-476.

We introduce different ways of modeling the dependency of the input noise of stochastic algorithms. We are aimed to prove that such innovations allow us to use the ODE (ordinary differential equation) method. Illustrations in the linear regression framework and in the law of the large number for triangular arrays of weighted dependent random variables are also given. We have aimed to provide results easy to check in practice.

La dépendance du bruit d'un algorithme stochastique est modélisée de différentes manières, de sorte que la méthode de l'équation différentielle ordinaire reste applicable. Ces techniques de dépendance faible sont illustrées ici par des applications à un algorithme de régression linéaire et à l'étude de tableaux triangulaires de variables aléatoires pondérées dépendantes. L'objectif est ici d'obtenir des conditions aisément vérifiables en pratique.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2003.07.002
Doukhan, Paul 1; Brandière, Odile 2

1 LS CREST, timbre J340, 3, avenue Pierre Larousse, 92240 Malakoff, France
2 Université Paris 11, laboratoire de mathématiques, bât. 425, 91405 Orsay, France
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Doukhan, Paul; Brandière, Odile. Algorithmes stochastiques à bruit dépendant. Comptes Rendus. Mathématique, Volume 337 (2003) no. 7, pp. 473-476. doi : 10.1016/j.crma.2003.07.002. http://www.numdam.org/articles/10.1016/j.crma.2003.07.002/

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