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Functional and random central limit theorems for the Robbins-Munro process

Published online by Cambridge University Press:  14 July 2016

D. L. McLeish
D. L. McLeish*
Affiliation:
York University, Downsview, Ontario
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Abstract

A functional central limit theorem extending the central limit theorem of Chung (1954) for the Robbins–Munro procedure is proved. It is shown that the asymptotic normality is preserved under certain random stopping rules.

Keywords

DONSKER'S THEOREMINVARIANCE PRINCIPLESTOCHASTIC APPROXIMATIONROBBINS–MUNRO PROCEDUREMARTINGALECENTRAL LIMIT THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 1 , March 1976 , pp. 148 - 154
Copyright
Copyright © Applied Probability Trust 1976 

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