A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains
type: Item
instance of: scholarly article
title: A uniform estimate for the rate of convergence in the multidimensional central limit theorem for homogeneous Markov chains
zbMATH Open document ID: 0853.60023
DOI: 10.1155/S0161171296000634
author: Yanyan Li
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1997-01-05T00:00:00Z
full work available at URL: https://eudml.org/doc/47559
review text: A uniform estimate is obtained for the remainder term in the central limit theorem (CLT) for a sequence of random vectors \(f(x_1), f(x_2), \dots\) forming a homogeneous Markov chain with arbitrary set of states. This estimate is obtained for \(\sup_{A\in B^k_0} |P_n- \Phi (A)|\) without assumption of the finiteness of \(\sup_{\xi\in X} \int_X |f(\eta) |^3 P(\xi, d\eta)\). CLT for sequences of random vectors \(f(x_1), f(x_2), \dots\) with condition of finiteness of the absolute second moment of the transition probabilities is proved, too.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 894075
zbMATH Keywords: rate of convergence
zbMATH Keywords: uniform estimate
zbMATH Keywords: remainder term in the central limit theorem
zbMATH Keywords: homogeneous Markov chain
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 894075