Geodesic
Adaptive energy-saving approximation for stationary processes
Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 932-956

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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.
Keywords: least-energy approximation, prediction, stationary process, stationary sequence. 
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     author = {Z. Kabluchko and M. A. Lifshits},
     title = {Adaptive energy-saving approximation for stationary processes},
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     pages = {932--956},
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     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a1/}
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Z. Kabluchko; M. A. Lifshits. Adaptive energy-saving approximation for stationary processes. Izvestiya. Mathematics , Tome 83 (2019) no. 5, pp. 932-956. http://geodesic.mathdoc.fr/item/IM2_2019_83_5_a1/