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.
Citation
Ray Cheng. "The Spectral Measure of a Regular Stationary Random Field with the Weak or Strong Commutation Property." Ann. Probab. 21 (3) 1263 - 1274, July, 1993. https://doi.org/10.1214/aop/1176989117
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