Search results for "Stable Processes"

showing 2 items of 2 documents

Spectral Density Estimate for Stable Processes Observed with an Additive Error

2018

International audience; In this paper, a symmetric alpha stable process where its spectral representation has an additive error is considered. The error is supposed to be constant. A periodogram as estimator of the spectral density and its rate of convergence are given. In order to give an asymptotically unbiased and consistent estimate of the spectral density, this periodogram is smoothed by an adapted spectral window. The rate of convergence is given.

Health (social science)General Computer ScienceAdditive errorGeneral MathematicsSpectral DensityStable Processes01 natural sciencesEducationStable process[SPI]Engineering Sciences [physics][MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]0103 physical sciencesStatistical physics[MATH]Mathematics [math]PeriodogramGeneral Environmental ScienceMathematics010308 nuclear & particles physicsSpectral windowGeneral EngineeringEstimatorSpectral density[STAT]Statistics [stat]General EnergyRate of convergencePeriodogramConstant (mathematics)[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]Advanced Science Letters
researchProduct

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

2006

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 periodicall…

[ 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 spectrale
researchProduct