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Maximal inequalities via bracketing with adaptive truncation. (English) Zbl 1019.60015

A recursive interpretation for the technique (bracketing with adaptive truncation) is provided. A simple bound is derived for the expected value of the supremum of an empirical process. This leads to a simpler derivation of a functional central limit theorem under less number of assumptions about processes and functionals indexed by sets of functions.

MSC:

60E15 Inequalities; stochastic orderings
60G07 General theory of stochastic processes
60F17 Functional limit theorems; invariance principles
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