Michael Voit
Abstract
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Using a slight generalisation of Brown's inequality, we show that for martingales the existence of a weak nonuniform bound on the rate of convergence in the central limit theorem yields the usual upper bound part of the law of the iterated logarithm.
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Using a slight generalisation of Brown's inequality, we show that for martingales the existence of a weak nonuniform bound on the rate of convergence in the central limit theorem yields the usual upper bound part of the law of the iterated logarithm.
Key concepts: Law of the iterated logarithm, Mathematics, Iterated logarithm, Logarithm, Central limit theorem, Upper and lower bounds, Rate of convergence, Iterated function