A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique decomposition of a stationary stable process into three independent stationary parts is obtained. It is shown that the dissipative part of a flow generates a mixed moving average part of a stationary stable process, while the identity part of a flow essentially gives the harmonizable part. The third part of a stationary process is determined by a conservative flow without fixed points and by a related cocycle.
@article{1176988178,
author = {Rosinski, Jan},
title = {On the Structure of Stationary Stable Processes},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 1163-1187},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988178}
}
Rosinski, Jan. On the Structure of Stationary Stable Processes. Ann. Probab., Tome 23 (1995) no. 3, pp. 1163-1187. http://gdmltest.u-ga.fr/item/1176988178/