Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Linear time-invariant transformations of some nonstationary random processes


Authors: D. Tjøstheim and J. B. Thomas
Journal: Quart. Appl. Math. 34 (1976), 113-117
MSC: Primary 60G99
DOI: https://doi.org/10.1090/qam/448551
MathSciNet review: 448551
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Abstract: We consider the class of nonstationary processes $ Y\left( t \right)$ which can be represented as $ Y\left( t \right) = BX\left( t \right)$, where $ X\left( t \right)$ is wide sense stationary and $ B$ is a bounded self-adjoint operator with a bounded inverse. An equivalent characterization of this class of processes is given and is used to construct examples of nonstationary processes belonging to this class. A functional analytic treatment is given for describing the effects of linear time-invariant transformations.


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DOI: https://doi.org/10.1090/qam/448551
Article copyright: © Copyright 1976 American Mathematical Society


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