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.
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.
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@article{CRMATH_2003__337_7_473_0,
author = {Doukhan, Paul and Brandi\`ere, Odile},
title = {Algorithmes stochastiques \`a bruit d\'ependant},
journal = {Comptes Rendus. Math\'ematique},
pages = {473--476},
publisher = {Elsevier},
volume = {337},
number = {7},
year = {2003},
doi = {10.1016/j.crma.2003.07.002},
language = {fr},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2003.07.002/}
}
TY - JOUR AU - Doukhan, Paul AU - Brandière, Odile TI - Algorithmes stochastiques à bruit dépendant JO - Comptes Rendus. Mathématique PY - 2003 SP - 473 EP - 476 VL - 337 IS - 7 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2003.07.002/ DO - 10.1016/j.crma.2003.07.002 LA - fr ID - CRMATH_2003__337_7_473_0 ER -
%0 Journal Article %A Doukhan, Paul %A Brandière, Odile %T Algorithmes stochastiques à bruit dépendant %J Comptes Rendus. Mathématique %D 2003 %P 473-476 %V 337 %N 7 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2003.07.002/ %R 10.1016/j.crma.2003.07.002 %G fr %F CRMATH_2003__337_7_473_0
Doukhan, Paul; Brandière, Odile. Algorithmes stochastiques à bruit dépendant. Comptes Rendus. Mathématique, Tome 337 (2003) no. 7, pp. 473-476. doi : 10.1016/j.crma.2003.07.002. http://archive.numdam.org/articles/10.1016/j.crma.2003.07.002/
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