Search results for "stable processe"
showing 4 items of 4 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.
Aliasing-Free and Additive Error in Mixed Spectra for Stable Processes. Application: Sound of a Bird just captivated in stress
2022
Consider a symmetric continuous time α stableprocess observed with an additive constant error. Theobjective of this paper is to give a non-parametric estimatorof this error by using discrete observations. As the time ofprocess is continuous and the observations are discrete, weencountered the aliasing phenomenon. Our process sampleis taken in a way to circumvent the difficulty related toaliasing and we smoothed the periodogram by using JacksonKernel. The rate of convergence of this estimator is studiedwhen the spectral density is zero at origin. Few long memoryprocesses are taken here as examples. We have applied ourestimator to the concrete case of modeling noise of a birdcaptured under st…
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…
Itô calculus extended to systems driven by -stable Lévy white noises (a novel clip on the tails of Lévy motion)
2007
Abstract The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Levy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Levy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Ito calculus extended to Poissonian input, may also be used for α -stable Levy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Levy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these c…