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Some extensions of linear approximation and prediction problems for stationary processes
Russian Acad Sci, Russia; St Petersburg State Univ, Russia.
Munster Univ, Germany.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. St Petersburg State Univ, Russia.
2019 (English)In: Stochastic Processes and their Applications, ISSN 0304-4149, E-ISSN 1879-209X, Vol. 129, no 8, p. 2758-2782Article in journal (Refereed) Published
Abstract [en]

Let (B(t))(t is an element of Theta) with Theta = Z or Theta = R be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in span{B(s), s amp;lt;= t} providing the best possible mean square approximation to the variable B(tau) with tau amp;gt; t. In this article we investigate this and some other similar problems where, in addition to prediction quality, optimization takes into account other features of the objects we search for. One of the most motivating examples of this kind is an approximation of a stationary process B by a stationary differentiable process X taking into account the kinetic energy that X spends in its approximation efforts. (C) 2018 Elsevier B.V. All rights reserved.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV , 2019. Vol. 129, no 8, p. 2758-2782
Keywords [en]
Energy saving approximation; Interpolation; Prediction; Wide sense stationary process
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-158923DOI: 10.1016/j.spa.2018.08.001ISI: 000473123800005OAI: oai:DiVA.org:liu-158923DiVA, id: diva2:1338203
Note

Funding Agencies|DFG-SPbSU grant [6.65.37.2017]; RFBR [16-01-00258]

Available from: 2019-07-20 Created: 2019-07-20 Last updated: 2019-07-20

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Lifshits, Mikhail
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Mathematical Statistics Faculty of Science & Engineering
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf