This work is concerned with the structural analysis of stationary
$\alpha$-stable random fields. Three distinct classes of such random fields are
characterized and it is shown that every stationary $\alpha$-stable random
field can be uniquely decomposed into the sum of three independent components
belonging to these classes. Various examples of stationary $\alpha$-stable
random fields are discussed in this context.
Publié le : 2000-10-14
Classification:
Stable random fields,
stationarity,
stochastic integral representation,
nonsingular flow,
cocycle,
mixed moving average,
harmonizable random field,
60G10,
60G07,
60E07,
60G57
@article{1019160508,
author = {Rosi{\'n}ski, Jan},
title = {Decomposition of stationary $\alpha$-stable random fields},
journal = {Ann. Probab.},
volume = {28},
number = {1},
year = {2000},
pages = { 1797-1813},
language = {en},
url = {http://dml.mathdoc.fr/item/1019160508}
}
Rosi{\'n}ski, Jan. Decomposition of stationary $\alpha$-stable random fields. Ann. Probab., Tome 28 (2000) no. 1, pp. 1797-1813. http://gdmltest.u-ga.fr/item/1019160508/