Doukhan, Paul; Brandière, Odile Algorithmes stochastiques à bruit dépendant (Dependent noise for stochastic algorithms). (French) Zbl 1039.60013 C. R., Math., Acad. Sci. Paris 337, No. 7, 473-476 (2003). Summary: 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 numbers for triangular arrays of weighted dependent random variables are also given. We have aimed to provide results easy to check in practice. Cited in 2 Documents MSC: 60E15 Inequalities; stochastic orderings Keywords:modeling the dependency of the input noise; ordinary differential equation method; linear regression; law of the large numbers for triangular arrays PDFBibTeX XMLCite \textit{P. Doukhan} and \textit{O. Brandière}, C. R., Math., Acad. Sci. Paris 337, No. 7, 473--476 (2003; Zbl 1039.60013) Full Text: DOI References: [1] Benaı̈m, M., A dynamical system approach to stochastic approximation, SIAM J. Control Optim., 34, 2, 437-472 (1996) · Zbl 0841.62072 [2] Chen, H.-F, Stochastic Approximation and Its Applications (2002), Kluwer Academic [3] Chow, Y. S., Some convergence theorems for independent random variables, Ann. Math. Statist., 37, 1482-1493 (1966), 36 (4) 1293-1314 · Zbl 0152.16905 [4] P. Dedecker, P. Doukhan, A new covariance inequality and applications, Stochastic Process. Appl. (2002), in press; P. Dedecker, P. Doukhan, A new covariance inequality and applications, Stochastic Process. Appl. (2002), in press · Zbl 1075.60513 [5] Delyon, B., General convergence result on stochastic approximation, IEEE Trans. Automatic Control, 41, 9 (1996) [6] Doukhan, P., Models inequalities and limit theorems for stationary sequences, (Doukhan; etal., Theory and Applications of Long Range Dependence (2002), Birkhäuser), 43-101 · Zbl 1032.62081 [7] Doukhan, P.; Louhichi, S., A new weak dependence condition and applications to moment inequalities, Stochastic Process. Appl., 84, 313-342 (1999) · Zbl 0996.60020 [8] Duflo, M., Algorithmes Stochastiques. Algorithmes Stochastiques, Collect. Math. Appl., 23 (1996), Springer [9] Kushner, H. J.; Clark, D. S., Stochastic Approximation for Constrained and Uncontrained Systems. Stochastic Approximation for Constrained and Uncontrained Systems, Appl. Math. Sci, 26 (1978), Springer This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.