Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the~$L^p$ norm, $2\le p\le\infty$
Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 453-467
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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.
@article{TMF_2012_173_3_a6,
author = {V. R. Fatalov},
title = {Asymptotic behavior of small deviations for {Bogoliubov's} {Gaussian} measure in the~$L^p$ norm, $2\le p\le\infty$},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {453--467},
publisher = {mathdoc},
volume = {173},
number = {3},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a6/}
}
TY - JOUR AU - V. R. Fatalov TI - Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the~$L^p$ norm, $2\le p\le\infty$ JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2012 SP - 453 EP - 467 VL - 173 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a6/ LA - ru ID - TMF_2012_173_3_a6 ER -
%0 Journal Article %A V. R. Fatalov %T Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the~$L^p$ norm, $2\le p\le\infty$ %J Teoretičeskaâ i matematičeskaâ fizika %D 2012 %P 453-467 %V 173 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a6/ %G ru %F TMF_2012_173_3_a6
V. R. Fatalov. Asymptotic behavior of small deviations for Bogoliubov's Gaussian measure in the~$L^p$ norm, $2\le p\le\infty$. Teoretičeskaâ i matematičeskaâ fizika, Tome 173 (2012) no. 3, pp. 453-467. http://geodesic.mathdoc.fr/item/TMF_2012_173_3_a6/