Displaying similar documents to “On the weak law of large numbers for normed weighted sums of i.i.d. random variables.”

Moderate deviations for I.I.D. random variables

Peter Eichelsbacher, Matthias Löwe (2003)

ESAIM: Probability and Statistics

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We derive necessary and sufficient conditions for a sum of i.i.d. random variables i = 1 n X i / b n – where b n n 0 , but b n n – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.