The Annals of Probability
- Ann. Probab.
- Volume 23, Number 3 (1995), 1163-1187.
On the Structure of Stationary Stable Processes
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.
Ann. Probab., Volume 23, Number 3 (1995), 1163-1187.
First available in Project Euclid: 19 April 2007
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Rosinski, Jan. On the Structure of Stationary Stable Processes. Ann. Probab. 23 (1995), no. 3, 1163--1187. doi:10.1214/aop/1176988178. https://projecteuclid.org/euclid.aop/1176988178