## The Annals of Probability

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

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

#### 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