| Issue |
ESAIM: PS
Volume 7, March 2003
|
|
|---|---|---|
| Page(s) | 209 - 218 | |
| DOI | https://doi.org/10.1051/ps:2003005 | |
| Published online | 15 May 2003 | |
Moderate Deviations for I.I.D. Random Variables
1
Ruhr-Universität Bochum,
Fakultät für Mathematik, NA3/68, 44780 Bochum, Germany; peter.eichelsbacher@ruhr-uni-bochum.de.
2
Department of Mathematics, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands; loewe@sci.kun.nl.
Received:
23
March
2002
Revised:
10
July
2002
We derive necessary and sufficient conditions for a sum of i.i.d.
random variables 
–
where 
,
but 
– 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.
Mathematics Subject Classification: 60F10
Key words: Moderate deviations / large deviations.
© EDP Sciences, SMAI, 2003
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