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February, 1995 A Wold-Like Decomposition of Two-Dimensional Discrete Homogeneous Random Fields
Joseph M. Francos, A. Zvi Meiri, Boaz Porat
Ann. Appl. Probab. 5(1): 248-260 (February, 1995). DOI: 10.1214/aoap/1177004839

Abstract

Imposing a total order on a regular two-dimensional discrete random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic field. The deterministic component is further orthogonally decomposed into a half-plane deterministic field and a countable number of mutually orthogonal evanescent fields. Each of the evanescent fields is generated by the column-to-column innovations of the deterministic field with respect to a different nonsymmetrical-half-plane total-ordering definition. The half-plane deterministic field has no innovations, nor column-to-column innovations, with respect to any nonsymmetrical-half-plane total-ordering definition. This decomposition results in a corresponding decomposition of the spectral measure of the regular random field into a countable sum of mutually singular spectral measures.

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Joseph M. Francos. A. Zvi Meiri. Boaz Porat. "A Wold-Like Decomposition of Two-Dimensional Discrete Homogeneous Random Fields." Ann. Appl. Probab. 5 (1) 248 - 260, February, 1995. https://doi.org/10.1214/aoap/1177004839

Information

Published: February, 1995
First available in Project Euclid: 19 April 2007

zbMATH: 0822.60045
MathSciNet: MR1325052
Digital Object Identifier: 10.1214/aoap/1177004839

Subjects:
Primary: 60G60
Secondary: 60G25

Keywords: deterministic random fields , evanescent random fields , purely indeterministic random fields , Two-dimensional random fields , two-dimensional spectral measures , two-dimensional Wold decomposition

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.5 • No. 1 • February, 1995
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