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THE SECOND CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE ARRAYS

  • Bae, Jongsig ;
  • Jun, Doobae ;
  • Levental, Shlomo
  • Received : 2011.08.12
  • Published : 2014.03.31

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

References

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