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Asymptotic behavior for the Robbins–Monro process

Part of: Parametric inference Limit theorems

Published online by Cambridge University Press:  26 July 2018

Yu Miao  and
Manru Dong
Yu Miao*
Affiliation:
Henan Normal University
Manru Dong*
Affiliation:
Henan Normal University
*
* Postal address: College of Mathematics and Information Science, Henan Normal University, 46# East of Construction Road, Xinxiang, Henan, 453007, China.
* Postal address: College of Mathematics and Information Science, Henan Normal University, 46# East of Construction Road, Xinxiang, Henan, 453007, China.
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Abstract

In this paper we study the Robbins–Monro procedure Xn+1 = Xn - an-1Yn with some fixed number a > 0 and establish the moderate deviation principle of the process {Xn}.

Keywords

Robbins–Monro processmoderate deviationexponential inequality

MSC classification

Primary: 62F12: Asymptotic properties of estimators
Secondary: 60F10: Large deviations
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 559 - 570
Copyright
Copyright © Applied Probability Trust 2018 

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