A uniform CLT for uniformly bounded families of martingale differences |
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Authors: | Shlomo Levental |
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Institution: | (1) Department of Statistics & Probability, Michigan State University, 48824 East Lansing, Michigan |
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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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Keywords: | Martingales empirical central limit theorems Markov chains baker's transformation continuous Gaussian processes |
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