Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2011.08.12
  • Published : 2014.03.31
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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.

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References

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