THE SECOND CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE ARRAYS

초록

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 rnajorizing measures. The results of present paper generalize those for a sequence of stationary martingale differences. The results also generalize independent problems.

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