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Harmonizable stable fields: Regularity and Wold-type decompositions

Author: David A. Redett
Journal: Proc. Amer. Math. Soc. 146 (2018), 831-844
MSC (2010): Primary 60G60, 60G52
Published electronically: October 12, 2017
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Abstract: In this article, we examine the structure of harmonizable stable fields. We start by examining horizontal and vertical regularity. We find equivalent conditions for horizontal and vertical regularity in terms of the harmonizable stable field's spectral measure. We then give a Wold-type decomposition in this setting. After that, we consider strong regularity. Here too, we give equivalent conditions for strong regularity in terms of the field's spectral measure. In addition, we show that strong regularity is equivalent to the field's ability to be represented by a moving average random field. We finish this article with a four-fold Wold-type decomposition.

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Additional Information

David A. Redett
Affiliation: Department of Mathematical Sciences, IPFW, 2101 E. Coliseum Boulevard, Fort Wayne, Indiana 46805-1499
Address at time of publication: Department of Mathematics, Terra State Community College, 2830 Napoleon Road, Fremont, Ohio 43420

Keywords: Harmonizable stable fields, regularity, Wold-type decompositions
Received by editor(s): July 2, 2016
Received by editor(s) in revised form: March 17, 2017
Published electronically: October 12, 2017
Communicated by: Mark M. Meerschaert
Article copyright: © Copyright 2017 American Mathematical Society

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