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Moderate Deviations for I.I.D. Random Variables

Published online by Cambridge University Press:  15 May 2003

Peter Eichelsbacher
Ruhr-Universität Bochum, Fakultät für Mathematik, NA3/68, 44780 Bochum, Germany;
Matthias Löwe
Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands;
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We derive necessary and sufficient conditions for a sum of i.i.d. random variables $\sum_{i=1}^n X_i/b_n$ – where $\frac {b_n} n \downarrow 0$, but $\frac {b_n} {\sqrt n} \uparrow \infty$ – 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.

Research Article
© EDP Sciences, SMAI, 2003

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