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June, 1981 Rates of Convergence in the Martingale Central Limit Theorem
Peter Hall, C. C. Heyde
Ann. Probab. 9(3): 395-404 (June, 1981). DOI: 10.1214/aop/1176994413


We obtain a nonuniform estimate of the rate of convergence in the martingale central limit theorem for convergence to mixtures of normal distributions. The uniform rates of convergence obtained by several other authors are special cases of our nonuniform estimate. We also obtain a rate of convergence in B. M. Brown's central limit theorem, assuming only Brown's elementary conditions. This result is a martingale analogue of Feller's generalization of the Berry-Esseen theorem.


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Peter Hall. C. C. Heyde. "Rates of Convergence in the Martingale Central Limit Theorem." Ann. Probab. 9 (3) 395 - 404, June, 1981.


Published: June, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0459.60042
MathSciNet: MR614625
Digital Object Identifier: 10.1214/aop/1176994413

Primary: 60G42

Keywords: G0F05 , martingale central limit theorem , mixtures of normal distributions , nonuniform bound , rate of convergence , uniform bound

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • June, 1981
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