Almost Sure Convergence for the Robbins-Monro Process
Goodsell, C. A. ; Hanson, D. L.
Ann. Probab., Tome 4 (1976) no. 6, p. 890-901 / Harvested from Project Euclid
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In this paper we investigate the almost sure convergence of the Robbins-Monro process $x_{n+1} = x_n - a_n(y_n - \alpha)$ under assumptions about the conditional distribution of $y_n$ given $x_n$ which involve the existence of first moments or something closely related. The process $x_n$ can converge almost surely even when the series $\sum^\infty_{n=1} a_n\lbrack y_n - E\{y_n\mid x_n\} \rbrack$ does not do so.
Publié le : 1976-12-14
Classification:  Stochastic approximation,  Robbins-Monro process,  62L20,  60G99 
@article{1176995934,
     author = {Goodsell, C. A. and Hanson, D. L.},
     title = {Almost Sure Convergence for the Robbins-Monro Process},
     journal = {Ann. Probab.},
     volume = {4},
     number = {6},
     year = {1976},
     pages = { 890-901},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995934}
}

Goodsell, C. A.; Hanson, D. L. Almost Sure Convergence for the Robbins-Monro Process. Ann. Probab., Tome 4 (1976) no. 6, pp.  890-901. http://gdmltest.u-ga.fr/item/1176995934/