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TMF, 2012, Volume 173, Number 3, Pages 453–467 (Mi tmf8338)  

This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$

V. R. Fatalov

Lomonosov Moscow State University, Moscow, Russia

Abstract: We prove several results on exact asymptotic formulas for small deviations in the $L^p$-norm with $2\le p\le\infty$ for Bogoliubov's stationary Gaussian process $\xi(t)$. We prove the property of mutual absolute continuity for the conditional Bogoliubov measure and the conditional Wiener measure and calculate the Radon–Nikodym derivative.

Keywords: small deviation, Bogoliubov measure, conditional Wiener measure

DOI: https://doi.org/10.4213/tmf8338

Full text: PDF file (513 kB)
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English version:
Theoretical and Mathematical Physics, 2012, 173:3, 1720–1733

Bibliographic databases:

Document Type: Article
Received: 21.03.2012

Citation: V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, TMF, 173:3 (2012), 453–467; Theoret. and Math. Phys., 173:3 (2012), 1720–1733

Citation in format AMSBIB
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Linking options:
  • http://mi.mathnet.ru/eng/tmf8338
  • https://doi.org/10.4213/tmf8338
  • http://mi.mathnet.ru/eng/tmf/v173/i3/p453

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. R. Fatalov, “Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$”, Problems Inform. Transmission, 50:4 (2014), 371–389  mathnet  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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