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December, 1978 A Weak Convergence Theorem with Application to the Robbins-Monro Process
Gotz D. Kersting
Ann. Probab. 6(6): 1015-1025 (December, 1978). DOI: 10.1214/aop/1176995390


In this paper the asymptotic distribution of a sequence of random variables $(X_n)_{n \in \mathbf{N}}$, given by the recursion $$X_{n+1} = X_n(1 - a_n^2g(X_n)) + a_n Y_n,$$ is considered, where $(Y_n)$ is a sequence of independent identically distributed random variables, $g : \mathbb{R} \rightarrow \mathbb{R}$ is a positive continuous function, and $(a_n)$ is a sequence of positive numbers, going to zero. One application to the Robbins-Monro process is discussed, in which the function $g$ will not be constant. Here the asymptotic distribution is no longer normal.


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Gotz D. Kersting. "A Weak Convergence Theorem with Application to the Robbins-Monro Process." Ann. Probab. 6 (6) 1015 - 1025, December, 1978.


Published: December, 1978
First available in Project Euclid: 19 April 2007

zbMATH: 0405.60019
MathSciNet: MR512417
Digital Object Identifier: 10.1214/aop/1176995390

Primary: 60F05
Secondary: 62L20

Keywords: Robbins-Monro process , weak convergence

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 6 • December, 1978
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