On Large Deviations in the Averaging Principle for Stochastic Differential Equations with "Complete Dependence"

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Previous article Next article On Large Deviations in the Averaging Principle for Stochastic Differential Equations with "Complete Dependence"A. Yu. VeretennikovA. Yu. Veretennikovhttps://doi.org/10.1137/S0040585X97977185PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe large deviation principle for a system of stochastic differential equations with fast and slow components is established in the case when the fast diffusion coefficient depends on a slow process.[1] Google Scholar[2] Google Scholar[3] A. Yu. Veretennikov, On large deviations in the averaging principle for stochastic differential equations with periodic coefficients, II, Math. USSR Izv., 39 (1992), pp. 677–701. axp MUSIAE 0025-5726 Math. USSR, Izv. CrossrefGoogle Scholar[4] Google Scholar[5] Google Scholar[6] M. I. Freidlin, Fluctuations in dynamical systems with averaging, Dokl. Akad. Nauk SSSR, 226 (1976), pp. 273–276 (in Russian). dan DANKAS 0002-3264 Dokl. Akad. Nauk SSSR Google Scholar[7] 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[8] Google ScholarKeywordslarge deviationsstochastic differential equationaveraging Previous article Next article FiguresRelatedReferencesCited ByDetails Averaging principle of SDE with small diffusion: Moderate deviationsThe Annals of Probability, Vol. 31, No. 1 | 1 Jan 2003 Cross Ref Moderate deviations of inhomogeneous functionals of Markov processes and application to averagingStochastic Processes and their Applications, Vol. 92, No. 2 | 1 Apr 2001 Cross Ref Volume 43, Issue 4| 1999Theory of Probability & Its Applications519-688 History Published online:25 July 2006 InformationCopyright © 1999 Society for Industrial and Applied MathematicsKeywordslarge deviationsstochastic differential equationaveragingPDF Download Article & Publication DataArticle DOI:10.1137/S0040585X97977185Article page range:pp. 664-666ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics