6533b839fe1ef96bd12a6276
RESEARCH PRODUCT
Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires
Nourddine Azzaouisubject
[ MATH ] Mathematics [math]Densité spectraleSpectral estimation[MATH] Mathematics [math]Estimation spectraleLepage Seriesnon-parametrique StatistiquesPeriodically covariated processesSéries de LepageSpectral AnalysisSpectral densityStrong mixing.Statistiques non paramétriquesMélange fortCovariationProcessus \alpha-stables[MATH]Mathematics [math]Mélange fort.Processus périodiquement covariés\alpha-stable ProcessesAnalyse spectraledescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-12-11 |