International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 441-450

A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains

M. Gharib

Mathematics Department, Faculty of Science, Qatar University, Qatar

Received 15 June 1994; Revised 17 January 1995

Copyright © 1996 M. Gharib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper a uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors forming a homogeneous Markov chain with arbitrary set of states. The result makes it possible to estimate the rate of convergence in the CLT without assuming the finiteness of the absolute third moment of the transition probabilities. Some consequences are also proved.