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January, 1988 On the Rate of Convergence in the Central Limit Theorem for Martingales with Discrete and Continuous Time
Erich Haeusler
Ann. Probab. 16(1): 275-299 (January, 1988). DOI: 10.1214/aop/1176991901

Abstract

Heyde and Brown (1970) established a bound on the rate of convergence in the central limit theorem for discrete time martingales having finite moments of order $2 + 2\delta$ with $0 < \delta \leq 1$. In the present paper a modification of the methods developed by Bolthausen (1982) is applied to show the validity of this result for all $\delta > 0$. Moreover, an example is constructed demonstrating that this bound is asymptotically exact for all $\delta > 0$. The result for discrete time martingales is then used to derive the corresponding bound on the rate of convergence in the central limit theorem for locally square integrable martingales with continuous time.

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Erich Haeusler. "On the Rate of Convergence in the Central Limit Theorem for Martingales with Discrete and Continuous Time." Ann. Probab. 16 (1) 275 - 299, January, 1988. https://doi.org/10.1214/aop/1176991901

Information

Published: January, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0639.60030
MathSciNet: MR920271
Digital Object Identifier: 10.1214/aop/1176991901

Subjects:
Primary: 60F05
Secondary: 60G42 , 60G44

Keywords: central limit theorem , Martingales with discrete and continuous time , rate of convergence

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 1 • January, 1988
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