[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2014.51.2.317

THE SECOND CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE ARRAYS

Bae, Jongsig (Department of Mathematics Institute of Basic Science Sungkyunkwan University)
Jun, Doobae (Department of Mathematics(and RING) Gyeongsang National University)
Levental, Shlomo (Department of Statistics and Probability Michigan State University)

Publication Information

Bulletin of the Korean Mathematical Society / v.51, no.2, 2014 , pp. 317-328 More about this Journal

Abstract

In Bae et al. [2], we have considered the uniform CLT for the 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;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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