It is shown in this paper that the sample paths of a Robbins-Monro process with harmonic coefficients may be approximated by weighted sums of independent, identically distributed random variables. A law of iterated logarithm and a weak invariance principle follow from this result.
Publié le : 1977-12-14
Classification:
Stochastic approximation,
approximation by independent random variables,
invariance principle,
60K99,
60G17,
60F05,
60F15
@article{1176995663,
author = {Kersting, Gotz},
title = {Almost Sure Approximation of the Robbins-Monro Process by Sums of Independent Random Variables},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 954-965},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995663}
}
Kersting, Gotz. Almost Sure Approximation of the Robbins-Monro Process by Sums of Independent Random Variables. Ann. Probab., Tome 5 (1977) no. 6, pp. 954-965. http://gdmltest.u-ga.fr/item/1176995663/