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Moderate deviations for I.I.D. random variables

Peter EichelsbacherMatthias Löwe — 2003

ESAIM: Probability and Statistics

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 n 0 , 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.

Process level moderate deviations for stabilizing functionals

Peter EichelsbacherTomasz Schreiber — 2010

ESAIM: Probability and Statistics


Functionals of spatial point process often satisfy a weak spatial dependence condition known as . In this paper we prove process level moderate deviation principles (MDP) for such functionals, which is a level-3 result for empirical point fields as well as a level-2 result for empirical point measures. The level-3 rate function coincides with the so-called specific information. We show that the general result can be applied to prove MDPs for various particular functionals, including random sequential...

Moderate Deviations for I.I.D. Random Variables

Peter EichelsbacherMatthias Löwe — 2010

ESAIM: Probability and Statistics

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 n 0 , 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.

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