Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
H. Djellout, A. Guillin, L. Wu (2006)
Annales de l'I.H.P. Probabilités et statistiques
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Moderate deviations of empirical periodogram and non-linear functionals of moving average processes
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We study the Gaussian random fields indexed by R whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal...
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