The Annals of Probability

Decomposition of stationary $\alpha$-stable random fields

Jan Rosi{\'n}ski

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Abstract

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.

Article information

Source
Ann. Probab., Volume 28, Number 4 (2000), 1797-1813.

Dates
First available in Project Euclid: 18 April 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1019160508

Digital Object Identifier
doi:10.1214/aop/1019160508

Mathematical Reviews number (MathSciNet)
MR1813849

Zentralblatt MATH identifier
1044.60039

Subjects
Primary: 60G10
Secondary: 60G07: General theory of processes 60E07: Infinitely divisible distributions; stable distributions 60G57: Random measures

Keywords
Stable random fields stationarity stochastic integral representation nonsingular flow cocycle mixed moving average harmonizable random field

Citation

Rosi{\'n}ski, Jan. Decomposition of stationary $\alpha$-stable random fields. Ann. Probab. 28 (2000), no. 4, 1797--1813. doi:10.1214/aop/1019160508. https://projecteuclid.org/euclid.aop/1019160508


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