The Annals of Probability

Exact Convergence Rates in Some Martingale Central Limit Theorems

E. Bolthausen

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Abstract

Convergence rates are derived in central limit theorems for martingale difference arrays. The rates depend heavily on the behavior of the conditional variances and on moment conditions. It is also shown that the rates which are obtained are the exact ones under the stated conditions.

Article information

Source
Ann. Probab., Volume 10, Number 3 (1982), 672-688.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993776

Digital Object Identifier
doi:10.1214/aop/1176993776

Mathematical Reviews number (MathSciNet)
MR659537

Zentralblatt MATH identifier
0494.60020

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G42: Martingales with discrete parameter

Keywords
Martingales central limit theorem rates of convergence

Citation

Bolthausen, E. Exact Convergence Rates in Some Martingale Central Limit Theorems. Ann. Probab. 10 (1982), no. 3, 672--688. doi:10.1214/aop/1176993776. https://projecteuclid.org/euclid.aop/1176993776


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