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TMF, 2010, Volume 165, Number 1, Pages 134–144 (Mi tmf6567)  

This article is cited in 9 scientific papers (total in 9 papers)

Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm

R. S. Pusev

St. Petersburg State University, St. Petersburg, Old Petershoff, Russia

Abstract: We obtain results on small deviations of Bogoliubov's Gaussian measure occurring in the theory of the statistical equilibrium of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of their small deviations with respect to a Hilbert norm.

Keywords: Bogoliubov measure, small deviation

DOI: https://doi.org/10.4213/tmf6567

Full text: PDF file (439 kB)
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English version:
Theoretical and Mathematical Physics, 2010, 165:1, 1348–1357

Bibliographic databases:

Received: 24.03.2010
Revised: 26.04.2010

Citation: R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, TMF, 165:1 (2010), 134–144; Theoret. and Math. Phys., 165:1 (2010), 1348–1357

Citation in format AMSBIB
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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. Nazarov A.I., Sheipak I.A., “Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes”, Bull. Lond. Math. Soc., 44:1 (2012), 12–24  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ya. Yu. Nikitin, R. S. Pusev, “The exact asymptotic of small deviations for a series of Brownian functionals”, Theory Probab. Appl., 57:1 (2013), 60–81  mathnet  crossref  crossref  zmath  isi  elib  elib
    3. V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, Theoret. and Math. Phys., 173:3 (2012), 1720–1733  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    4. A. I. Nazarov, R. S. Pusev, “Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms”, St. Petersburg Math. J., 25:3 (2014), 455–466  mathnet  crossref  mathscinet  zmath  isi  elib
    5. 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
    6. Lifshits M., Nazarov A., “L-2-Small Deviations For Weighted Stationary Processes”, Mathematika, 64:2 (2018), 387–405  crossref  mathscinet  zmath  isi
    7. Nazarov A.I., Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55  crossref  zmath  isi  scopus
    8. 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
    9. Ibragimov I.A., Lifshits M.A., Nazarov A.I., Zaporozhets D.N., “On the History of St. Petersburg School of Probability and Mathematical Statistics: II. Random Processes and Dependent Variables”, Vestn. St Petersb. Univ.-Math., 51:3 (2018), 213–236  crossref  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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