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July 1996 A note on exact convergence rates in some martingale central limit theorems
Joachim Renz
Ann. Probab. 24(3): 1616-1637 (July 1996). DOI: 10.1214/aop/1065725195

Abstract

Bolthausen established a bound of order $1/\sqrt{n}$ on the rate of convergence in the central limit theorem for martingale difference arrays having bounded conditional moments of order 4. In the present paper it is shown how much this moment condition can be relaxed while maintaining the same rate of convergence. An example shows that, unlike in the i.i.d. case, a moment condition of order 3 is not enough. Furthermore, exact rates of convergence are derived for moment conditions of order between 2 and 3.

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Joachim Renz. "A note on exact convergence rates in some martingale central limit theorems." Ann. Probab. 24 (3) 1616 - 1637, July 1996. https://doi.org/10.1214/aop/1065725195

Information

Published: July 1996
First available in Project Euclid: 9 October 2003

zbMATH: 0868.60015
MathSciNet: MR1411508
Digital Object Identifier: 10.1214/aop/1065725195

Subjects:
Primary: 60F05, 60G42

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.24 • No. 3 • July 1996
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