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TMF, 2008, Volume 157, Number 2, Pages 286–308 (Mi tmf6280)  

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

Some asymptotic formulas for the Bogoliubov Gaussian measure

V. R. Fatalov

M. V. Lomonosov Moscow State University

Abstract: We consider problems of integrating over the Bogoliubov measure in the space of continuous functions and obtain asymptotic formulas for one class of Laplace-type functional integrals with respect to the Bogoliubov measure. We also prove related asymptotic results concerning large deviations for the Bogoliubov measure. For the basic functional, we take the $L^p$ norm and establish that the Bogoliubov trajectories are Hölder-continuous of order $\gamma<1/2$.

Keywords: Bogoliubov measure, Laplace method in a Banach space

DOI: https://doi.org/10.4213/tmf6280

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English version:
Theoretical and Mathematical Physics, 2008, 157:2, 1606–1625

Bibliographic databases:

Received: 19.07.2007

Citation: V. R. Fatalov, “Some asymptotic formulas for the Bogoliubov Gaussian measure”, TMF, 157:2 (2008), 286–308; Theoret. and Math. Phys., 157:2 (2008), 1606–1625

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v157/i2/p286

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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. R. S. Pusev, “Asymptotics of small deviations of the Bogoliubov processes with respect to a quadratic norm”, Theoret. and Math. Phys., 165:1 (2010), 1348–1357  mathnet  crossref  crossref  adsnasa  isi
    2. V. R. Fatalov, “Laplace-type exact asymptotic formulas for the Bogoliubov Gaussian measure”, Theoret. and Math. Phys., 168:2 (2011), 1112–1149  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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