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.
@article{PS_2003__7__209_0, author = {Eichelsbacher, Peter and L\"owe, Matthias}, title = {Moderate deviations for {I.I.D.} random variables}, journal = {ESAIM: Probability and Statistics}, pages = {209--218}, publisher = {EDP-Sciences}, volume = {7}, year = {2003}, doi = {10.1051/ps:2003005}, mrnumber = {1956079}, zbl = {1019.60021}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2003005/} }
TY - JOUR AU - Eichelsbacher, Peter AU - Löwe, Matthias TI - Moderate deviations for I.I.D. random variables JO - ESAIM: Probability and Statistics PY - 2003 SP - 209 EP - 218 VL - 7 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2003005/ DO - 10.1051/ps:2003005 LA - en ID - PS_2003__7__209_0 ER -
Eichelsbacher, Peter; Löwe, Matthias. Moderate deviations for I.I.D. random variables. ESAIM: Probability and Statistics, Tome 7 (2003), pp. 209-218. doi : 10.1051/ps:2003005. http://www.numdam.org/articles/10.1051/ps:2003005/
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