Abstract
This paper develops a method to get empirical central limit theorems for martingale differences that are uniformly bounded. The main idea is to generalize to martingales some ideas of E. Gine and J. Zinn [Ann. Prob. 12, 929–989 (1984)]. We consider two examples: An extension of a theorem of R. Dudley from i.i.d. to a certain type of Markov chain, and a uniform CLT for the “baker's transformation”.
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Levental, S. A uniform CLT for uniformly bounded families of martingale differences. J Theor Probab 2, 271–287 (1989). https://doi.org/10.1007/BF01054016
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DOI: https://doi.org/10.1007/BF01054016