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

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Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 165, Number 1, Pages 134–144
DOI: https://doi.org/10.4213/tmf6567 (Mi tmf6567)

This article is cited in 11 scientific papers (total in 11 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

Full-text PDF (439 kB) Citations (11)

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

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.

Received: 24.03.2010
Revised: 26.04.2010

English version:
Theoretical and Mathematical Physics, 2010, Volume 165, Issue 1, Pages 1348–1357
DOI: https://doi.org/10.1007/s11232-010-0113-4

Bibliographic databases:

Document Type: Article

Language: Russian

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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Linking options:

https://www.mathnet.ru/eng/tmf6567

https://doi.org/10.4213/tmf6567

https://www.mathnet.ru/eng/tmf/v165/i1/p134

This publication is cited in the following 11 articles:

Alexander Nazarov, Yulia Petrova, “L2-small ball asymptotics for Gaussian random functions: A survey”, Probab. Surveys, 20:none (2023)
Rozovsky L.V., “Small Deviation Probabilities For Sums of Independent Positive Random Variables”, Vestn. St Petersb. Univ.-Math., 53:3 (2020), 295–307
Lifshits M., Nazarov A., “L-2-Small Deviations For Weighted Stationary Processes”, Mathematika, 64:2 (2018), 387–405
Nazarov A.I., Nikitin Ya.Yu., “On Small Deviation Asymptotics in l-2 of Some Mixed Gaussian Processes”, 6, no. 4, 2018, 55
V. R. Fatalov, “Functional integrals for the Bogoliubov Gaussian measure: Exact asymptotic forms”, Theoret. and Math. Phys., 195:2 (2018), 641–657
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
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
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
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
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
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

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

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