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July, 1995 On the Structure of Stationary Stable Processes
Jan Rosinski
Ann. Probab. 23(3): 1163-1187 (July, 1995). DOI: 10.1214/aop/1176988178


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.


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Jan Rosinski. "On the Structure of Stationary Stable Processes." Ann. Probab. 23 (3) 1163 - 1187, July, 1995.


Published: July, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0836.60038
MathSciNet: MR1349166
Digital Object Identifier: 10.1214/aop/1176988178

Primary: 60G10
Secondary: 60E07 , 60G07 , 60G57

Keywords: Cocycle , harmonizable process , Hopf decomposition , mixed moving average , nonsingular flow , ‎spectral representation , Stationary stable process

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • July, 1995
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