Open Access
August, 1982 Exact Convergence Rates in Some Martingale Central Limit Theorems
E. Bolthausen
Ann. Probab. 10(3): 672-688 (August, 1982). DOI: 10.1214/aop/1176993776


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.


Download Citation

E. Bolthausen. "Exact Convergence Rates in Some Martingale Central Limit Theorems." Ann. Probab. 10 (3) 672 - 688, August, 1982.


Published: August, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0494.60020
MathSciNet: MR659537
Digital Object Identifier: 10.1214/aop/1176993776

Primary: 60F05
Secondary: 60G42

Keywords: central limit theorem , Martingales , rates of convergence

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • August, 1982
Back to Top