Moderate deviations for I.I.D. random variables
ESAIM: Probability and Statistics, Volume 7  (2003), p. 209-218

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 n0, 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.

DOI : https://doi.org/10.1051/ps:2003005
Classification:  60F10
Keywords: moderate deviations, large deviations
@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},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2003},
     pages = {209-218},
     doi = {10.1051/ps:2003005},
     zbl = {1019.60021},
     mrnumber = {1956079},
     language = {en},
     url = {http://www.numdam.org/item/PS_2003__7__209_0}
}
Eichelsbacher, Peter; Löwe, Matthias. Moderate deviations for I.I.D. random variables. ESAIM: Probability and Statistics, Volume 7 (2003) , pp. 209-218. doi : 10.1051/ps:2003005. http://www.numdam.org/item/PS_2003__7__209_0/

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