Open Access
Translator Disclaimer
December, 1976 Almost Sure Convergence for the Robbins-Monro Process
C. A. Goodsell, D. L. Hanson
Ann. Probab. 4(6): 890-901 (December, 1976). DOI: 10.1214/aop/1176995934

Abstract

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.

Citation

Download Citation

C. A. Goodsell. D. L. Hanson. "Almost Sure Convergence for the Robbins-Monro Process." Ann. Probab. 4 (6) 890 - 901, December, 1976. https://doi.org/10.1214/aop/1176995934

Information

Published: December, 1976
First available in Project Euclid: 19 April 2007

zbMATH: 0351.62061
MathSciNet: MR431560
Digital Object Identifier: 10.1214/aop/1176995934

Subjects:
Primary: 62L20
Secondary: 60G99

Rights: Copyright © 1976 Institute of Mathematical Statistics

JOURNAL ARTICLE
12 PAGES


SHARE
Vol.4 • No. 6 • December, 1976
Back to Top