Previous article Next article On Large Deviations for Stochastic DifferentialEquations with a Small Diffusion and AveragingA. Yu. VeretennikovA. Yu. Veretennikovhttps://doi.org/10.1137/S0040585X97976969PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThis paper states the large deviations principle for a system of stochastic equations with "fast" and "slow" variables and a small diffusion in a "slow" component.[1] M. D. Donsker and and S. R. S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large time, IV, Comm. Pure Appl. Math., 36 (1983), pp. 183–212. cpa CPMAMV 0010-3640 Commun. Pure Appl. Math. CrossrefGoogle Scholar[2] M. I. Freidlin, The averaging principle and theorems on large deviations, Uspekhi Mat. Nauk, 33 (1978), pp. 107–160 (in Russian). umn UMANA5 0042-1316 Usp. Mat. Nauk Google Scholar[3] Google Scholar[4] Google Scholar[5] Google Scholar[6] Google Scholar[7] R. Sh. Liptser, Large deviations for two‐scaled diffusions, Probab. Theory Related Fields, 106 (1996), pp. 71–104. aj9 PTRFEU 0178-8051 Probab. Theory Relat. Fields CrossrefGoogle Scholar[8] A. Yu. Veretennikov, Large deviations in averaging principle for stochastic differential equation systems (noncompact case), Stochastics Reports, 48 (1994), pp. 83–96. sso SSTREY 1045-1129 Stoch. Stoch. Rep. CrossrefGoogle Scholar[9] Google Scholar[10] A. Yu. Veretennikov, Lower bound for large deviations for an averaged SDE with a small diffusion, Russian J. Math. Phys., 5 (1997), pp. 99–104. afk RJMPEL 1061-9208 Russ. J. Math. Phys. Google ScholarKeywordslarge deviationsaveragingstochastic differential equation Previous article Next article FiguresRelatedReferencesCited byDetails On large deviations in the averaging principle for SDE's with a "full dependence,'' revisitedDiscrete and Continuous Dynamical Systems - Series B, Vol. 18, No. 2 Cross Ref Averaging principle of SDE with small diffusion: Moderate deviationsThe Annals of Probability, Vol. 31, No. 1 Cross Ref Déviations modérées pour la moyennisation d'une EDS avec petite diffusionComptes Rendus de l'Académie des Sciences - Series I - Mathematics, Vol. 332, No. 8 Cross Ref Volume 43, Issue 2| 1999Theory of Probability & Its Applications History Published online:25 July 2006 InformationCopyright © 1999 Society for Industrial and Applied MathematicsKeywordslarge deviationsaveragingstochastic differential equationPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97976969Article page range:pp. 335-337ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics