Harmonizable stable fields: Regularity and Wold-type decompositions

Redett, David

doi:10.1090/proc/13812

Harmonizable stable fields: Regularity and Wold-type decompositions
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by David A. Redett PDF

Proc. Amer. Math. Soc. 146 (2018), 831-844 Request permission

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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