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Journal of Statistical Theory and Practice

, Volume 5, Issue 3, pp 515–523 | Cite as

A Spectral Representation of a Class of Nonstationary Processes

  • Randall J. Swift
Article

Abstract

In this paper, an extension of the weakly harmonizable class of processes is considered. This class, termed almost periodic contractive harmonizable, is based upon the natural contractive operator associated with harmonizable processes. A spectral representation of these processes is obtained. A relation between the almost periodic contractive harmonizable and the oscillatory harmonizable classes is considered. The paper concludes with a series representation for the almost periodic contractive harmonizable class.

AMS Subject Classification

60G12 60G35 

Keywords

Harmonizable processes Oscillatory processes Semi-groups of contractive operators Almost periodic functions 

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Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsCalifornia State Polytechnic UniversityPomonaUSA

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