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Lithuanian Mathematical Journal

, Volume 54, Issue 1, pp 48–60 | Cite as

L 1 bounds for some martingale central limit theorems

  • Le Van DungEmail author
  • Ta Cong Son
  • Nguyen Duy Tien
Article

Abstract

The aim of this paper is to extend the results in [E. Bolthausen, Exact convergence rates in some martingale central limit theorems, Ann. Probab., 10(3):672–688, 1982] and [J.C. Mourrat, On the rate of convergence in the martingale central limit theorem, Bernoulli, 19(2):633–645, 2013] to the L1-distance between distributions of normalized partial sums for martingale-difference sequences and the standard normal distribution.

Keywords

mean central limit theorems rates of convergence martingale 

MSC

60F05 60G42 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsDa Nang University of EducationDa NangViet Nam
  2. 2.Faculty of MathematicsHanoi University of ScienceHanoiViet Nam

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