Bull. Korean Math. Soc. 2014; 51(2): 317-328
Printed March 31, 2014
https://doi.org/10.4134/BKMS.2014.51.2.317
Copyright © The Korean Mathematical Society.
Jongsig Bae, Doobae Jun, and Shlomo Levental
Sungkyunkwan University, Gyeongsang National University, Michigan State University
In Bae {\em et al.} \cite{ReferBJL}, we have considered the uniform CLT forthe martingale difference arrays under the uniformly integrable entropy. In this paper, we prove the same problem under the bracketing entropy condition. The proofs are based on Freedman inequality combined with a chaining argument that utilizes majorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.
Keywords: central limit theorem, martingale difference array, bracketing entropy, majorizing measure, eventual uniform equicontinuity
MSC numbers: Primary 60F17; Secondary 60F05
2014; 51(3): 701-716
2003; 40(4): 715-722
2010; 47(1): 39-51
2010; 47(6): 1139-1153
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