# Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires

Abstract : In this work a new spectral representation of a symmetric alpha-stable processes is introduced. It is based on a covariation pseudo-additivity and Morse-Transue's integral with respect to a bimesure built by using pseudo-additivity property. This representation, specific to S$\alpha$S processes, is analogous to the covariance of second order processes. On the other hand, it generalizes the representation established for stochastic integrals with respect to symmetric alpha-stable process of independent increments. We provide a classification of non-stationary harmonizable processes; this classification is based on the bimesure structure. In particular, we defined and investigated periodically covariated processes. To simulate and build this unusual class, a new decomposition in the Lepage's type series was derived. Finally, to apply this results in practical situations, a nonparametric estimation of spectral densities are discussed. In particular, in the case of periodically covariated processes, an almost sure convergent estimators was derived under the strong mixing condition.
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https://tel.archives-ouvertes.fr/tel-00138027
Contributor : Nourddine Azzaoui <>
Submitted on : Friday, March 23, 2007 - 9:58:20 AM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, April 7, 2010 - 12:26:20 AM

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• HAL Id : tel-00138027, version 1

### Citation

Nourddine Azzaoui. Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires. Mathématiques [math]. Université de Bourgogne, 2006. Français. ⟨tel-00138027⟩

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