It is shown that a regular stationary random field on $\mathbf{Z}^2$ exhibits the weak (strong) commutation property if and only if its spectral density is the squared modulus of a weakly (strongly) outer function in the Hardy space $H^2(\mathbf{T}^2)$ of the torus. Applications to prediction are discussed.
Publié le : 1993-07-14
Classification:
Stationary random field,
prediction theory,
commutation property,
outer function,
60G60,
60G25,
32A35
@article{1176989117,
author = {Cheng, Ray},
title = {The Spectral Measure of a Regular Stationary Random Field with the Weak or Strong Commutation Property},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1263-1274},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989117}
}
Cheng, Ray. The Spectral Measure of a Regular Stationary Random Field with the Weak or Strong Commutation Property. Ann. Probab., Tome 21 (1993) no. 4, pp. 1263-1274. http://gdmltest.u-ga.fr/item/1176989117/