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THE SECOND CENTRAL LIMIT THEOREM FOR MARTINGALE DIFFERENCE ARRAYSopen access
- Authors
- Bae, Jongsig; Jun, Doobae; Levental, Shlomo
- Issue Date
- Mar-2014
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- central limit theorem; martingale difference array; bracketing entropy; majorizing measure; eventual uniform equicontinuity
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.51, no.2, pp 317 - 328
- Pages
- 12
- Indexed
- SCIE
SCOPUS
KCI
- Journal Title
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 51
- Number
- 2
- Start Page
- 317
- End Page
- 328
- ISSN
- 1015-8634
2234-3016
- 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 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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