Open Access
October 2000 Decomposition of stationary $\alpha$-stable random fields
Jan Rosiński
Ann. Probab. 28(4): 1797-1813 (October 2000). DOI: 10.1214/aop/1019160508


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.


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Jan Rosiński. "Decomposition of stationary $\alpha$-stable random fields." Ann. Probab. 28 (4) 1797 - 1813, October 2000.


Published: October 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.60039
MathSciNet: MR1813849
Digital Object Identifier: 10.1214/aop/1019160508

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

Keywords: Cocycle , harmonizable random field , mixed moving average , nonsingular flow , Stable random fields , stationarity , stochastic integral representation

Rights: Copyright © 2000 Institute of Mathematical Statistics

Vol.28 • No. 4 • October 2000
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