Adaptive energy-saving approximation for stationary processes

We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining high quality approximation and other good properties that can be interpreted as additional smoothness or small expense of energy. The problem is solved in terms...

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Bibliographic Details
Published in:Izvestiya. Mathematics 2019-10, Vol.83 (5), p.932-956
Main Authors: Kabluchko, Z. A., Lifshits, M. A.
Format: Article
Language:English
Subjects:
Approximation
Energy conservation
least-energy approximation
Mathematical analysis
prediction
Smoothness
stationary process
Stationary processes
stationary sequence
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Summary:We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining high quality approximation and other good properties that can be interpreted as additional smoothness or small expense of energy. The problem is solved in terms of spectral characteristics of the original process using the classical analytic methods of prediction theory.
ISSN:1064-5632
1468-4810
DOI:10.1070/IM8840