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Least Energy Approximation for Processes with Stationary Increments
University of Munster, Germany.
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering. St Petersburg State University, Russia.
2017 (English)In: Journal of theoretical probability, ISSN 0894-9840, E-ISSN 1572-9230, Vol. 30, no 1, 268-296 p.Article in journal (Refereed) Published
Abstract [en]

A function is called least energy approximation to a function B on the interval [0, T] with penalty Q if it solves the variational problem integral(T)(0)[f(t)(2) + Q(f(t) - B(t))] dt SE arrow min. For quadratic penalty, the least energy approximation can be found explicitly. If B is a random process with stationary increments, then on large intervals, also is close to a process of the same class, and the relation between the corresponding spectral measures can be found. We show that in a long run (when ), the expectation of energy of optimal approximation per unit of time converges to some limit which we compute explicitly. For Gaussian and L,vy processes, we complete this result with almost sure and convergence. As an example, the asymptotic expression of approximation energy is found for fractional Brownian motion.

Place, publisher, year, edition, pages
SPRINGER/PLENUM PUBLISHERS , 2017. Vol. 30, no 1, 268-296 p.
Keyword [en]
Least energy approximation; Gaussian process; Levy process; Fractional Brownian motion; Process with stationary increments; Taut string; Variational calculus
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-136659DOI: 10.1007/s10959-015-0642-8ISI: 000395076700010OAI: oai:DiVA.org:liu-136659DiVA: diva2:1089760
Note

Funding Agencies| [NSh.2504.2014.1]; [RFBR 13-01-00172]; [SPbSU 6.38.672.2013]

Available from: 2017-04-20 Created: 2017-04-20 Last updated: 2017-04-20

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Lifshits, Mikhail
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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other style
More styles
Language
  • de-DE
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  • en-US
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  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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Output format
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