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Probl. Peredachi Inf., 2014, Volume 50, Issue 4, Pages 79–99 (Mi ppi2155)  

This article is cited in 3 scientific papers (total in 3 papers)

Large Systems

Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$

V. R. Fatalov

Laboratory of Probability, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

Abstract: We prove results on sharp asymptotics of probabilities
$$ \mathbf P\{\int_0^1|X(t)|^p dt<\varepsilon^p\},\qquad\varepsilon\to0, $$
where $0<p<\infty$, for three Gaussian processes $X(t)$, namely the stationary and nonstationary Ornstein–Uhlenbeck process and the Bogoliubov process. The analysis is based on the Laplace method for sojourn times of a Wiener process.

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English version:
Problems of Information Transmission, 2014, 50:4, 371–389

Bibliographic databases:

UDC: 621.391.1+519.2
Received: 17.09.2014

Citation: V. R. Fatalov, “Gaussian Ornstein–Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$”, Probl. Peredachi Inf., 50:4 (2014), 79–99; Problems Inform. Transmission, 50:4 (2014), 371–389

Citation in format AMSBIB
\Bibitem{Fat14}
\by V.~R.~Fatalov
\paper Gaussian Ornstein--Uhlenbeck and Bogoliubov processes: asymptotics of small deviations for $L^p$-functionals, $0<p<\infty$
\jour Probl. Peredachi Inf.
\yr 2014
\vol 50
\issue 4
\pages 79--99
\mathnet{http://mi.mathnet.ru/ppi2155}
\transl
\jour Problems Inform. Transmission
\yr 2014
\vol 50
\issue 4
\pages 371--389
\crossref{https://doi.org/10.1134/S0032946014040073}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920624590}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. Mayorov, J. Hristoskov, N. Balakrishnan, “On a Family of Weighted Cramer-Von Mises Goodness-of-Fit Tests in Operational Risk Modeling”, J. Oper. Risk., 12:2 (2017), 1–21  crossref  isi  scopus
    2. V. R. Fatalov, “Integrals of Bessel processes and multi-dimensional Ornstein–Uhlenbeck processes: exact asymptotics for $L^p$-functionals”, Izv. Math., 82:2 (2018), 377–406  mathnet  crossref  crossref  adsnasa  isi  elib
    3. V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657  mathnet  crossref  crossref  adsnasa  isi  elib
  • Проблемы передачи информации Problems of Information Transmission
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