Estimation of the spectral density of a homogeneous random stable discrete time field

In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discretetime random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homoge-neous symm...

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Bibliographic Details
Authors: Demesh, Nikolay N., Chekhmenok, Sergey L.
Format: article
Publication Date:2005
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2099/3756
Online Access:https://hdl.handle.net/2099/3756
Access Level:Open access
Keyword:Stochastic processes
Processos estocàstics
Classificació AMS::60 Probability theory and stochastic processes::60G Stochastic processes
Description
Summary:In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discretetime random fields having finite second-order moments. In this paper, we show that 2π-periodic spectral windows can also be used to construct estimates of the spectral density of a homoge-neous symmetric α-stable discrete-time random field. These fields do not have second-order moments if 0 < α < 2. We construct an estimate of the spectrum, calculate the asymptotic mean and variance, and prove weak consistency of our estimate.