Moderate deviations for non-linear functionals and empirical spectral density of moving average processes

Details Moderate deviations for non-linear functionals and empirical spectral density of moving average processes Moderate deviations for non-linear functionals and empirical spectral density of moving average processes

2004-05-27

arxiv.org/abs/math/0405521v1

Mathematics

Probability

Scientific paper

A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random variables and the continuity, or weaker, of the spectral density of the moving average process. We also obtain the moderate deviations for the empirical spectral density, exhibiting an interesting new form of the rate function, i.e. with a correction term compared to the Gaussian rate functionnal.

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