## The Annals of Probability

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

Ray Cheng

#### 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

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