Moderate deviations for I.I.D. random variables

Eichelsbacher, Peter; Löwe, Matthias

doi:10.1051/ps:2003005

Eichelsbacher, Peter ; Löwe, Matthias

ESAIM: Probability and Statistics, Tome 7 (2003), pp. 209-218.

Résumé

We derive necessary and sufficient conditions for a sum of i.i.d. random variables $\sum_{i = 1}^{n} X_{i} / b_{n}$ - where $\frac{b_{n}}{n} ↓ 0$ , but $\frac{b_{n}}{\sqrt{n}} ↑ \infty$ - 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.

MR Zbl | 2 citations dans Numdam

DOI : 10.1051/ps:2003005

Classification : 60F10
Mots-clés : moderate deviations, large deviations

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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://archive.numdam.org/articles/10.1051/ps:2003005/

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