In earlier papers, 2π-periodic spectral data windows have been used in spectral estimation of discrete- time 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 homogeneous 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.
@article{urn:eudml:doc:40468,
title = {Estimation of the spectral density of a homogeneous random stable discrete time field.},
journal = {SORT},
volume = {29},
year = {2005},
pages = {101-118},
mrnumber = {MR2160538},
zbl = {1274.60161},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40468}
}
Demesh, Nicolay N.; Chekhmenok, Sergey L. Estimation of the spectral density of a homogeneous random stable discrete time field.. SORT, Tome 29 (2005) pp. 101-118. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40468/