The Annals of Probability

The Spectral Measure of a Regular Stationary Random Field with the Weak or Strong Commutation Property

Ray Cheng

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Abstract

It is shown that a regular stationary random field on $\mathbf{Z}^2$ exhibits the weak (strong) commutation property if and only if its spectral density is the squared modulus of a weakly (strongly) outer function in the Hardy space $H^2(\mathbf{T}^2)$ of the torus. Applications to prediction are discussed.

Article information

Source
Ann. Probab., Volume 21, Number 3 (1993), 1263-1274.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176989117

Digital Object Identifier
doi:10.1214/aop/1176989117

Mathematical Reviews number (MathSciNet)
MR1235415

Zentralblatt MATH identifier
0790.60038

JSTOR
links.jstor.org

Subjects
Primary: 60G60: Random fields
Secondary: 60G25: Prediction theory [See also 62M20] 32A35: Hp-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]

Keywords
Stationary random field prediction theory commutation property outer function

Citation

Cheng, Ray. The Spectral Measure of a Regular Stationary Random Field with the Weak or Strong Commutation Property. Ann. Probab. 21 (1993), no. 3, 1263--1274. doi:10.1214/aop/1176989117. https://projecteuclid.org/euclid.aop/1176989117


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