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

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

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English version:
Theoretical and Mathematical Physics, 2010, 165:1, 1348–1357

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Document Type: Article
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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• http://mi.mathnet.ru/eng/tmf/v165/i1/p134

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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. 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
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
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
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
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
6. Lifshits M., Nazarov A., “L-2-Small Deviations For Weighted Stationary Processes”, Mathematika, 64:2 (2018), 387–405
7. Nazarov A.I., Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55
8. V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657
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
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