The Annals of Probability

Almost Sure Approximation of the Robbins-Monro Process by Sums of Independent Random Variables

Gotz Kersting

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Abstract

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.

Article information

Source
Ann. Probab., Volume 5, Number 6 (1977), 954-965.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176995663

Digital Object Identifier
doi:10.1214/aop/1176995663

Mathematical Reviews number (MathSciNet)
MR494741

Zentralblatt MATH identifier
0374.62082

JSTOR
links.jstor.org

Subjects
Primary: 60K99: None of the above, but in this section
Secondary: 60G17: Sample path properties 60F05: Central limit and other weak theorems 60F15: Strong theorems

Keywords
Stochastic approximation approximation by independent random variables invariance principle

Citation

Kersting, Gotz. Almost Sure Approximation of the Robbins-Monro Process by Sums of Independent Random Variables. Ann. Probab. 5 (1977), no. 6, 954--965. doi:10.1214/aop/1176995663. https://projecteuclid.org/euclid.aop/1176995663


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