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Teoreticheskaya i Matematicheskaya Fizika, 2012, Volume 173, Number 3, Pages 453–467
DOI: https://doi.org/10.4213/tmf8338 (Mi tmf8338) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$

V. R. Fatalov

Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf8338
Abstract: We prove several results on exact asymptotic formulas for small deviations in the $L^p$-norm with $2\le p\le\infty$ for Bogoliubov's stationary Gaussian process $\xi(t)$. We prove the property of mutual absolute continuity for the conditional Bogoliubov measure and the conditional Wiener measure and calculate the Radon–Nikodym derivative.
Keywords: small deviation, Bogoliubov measure, conditional Wiener measure.
Received: 21.03.2012
English version:
Theoretical and Mathematical Physics, 2012, Volume 173, Issue 3, Pages 1720–1733
DOI: https://doi.org/10.1007/s11232-012-0143-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. R. Fatalov, “Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the $L^p$ norm, $2\le p\le\infty$”, TMF, 173:3 (2012), 453–467; Theoret. and Math. Phys., 173:3 (2012), 1720–1733
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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