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On large deviations in the averaging principle for SDE's with a "full dependence,'' revisited
1.  School of Mathematics, University of Leeds, LS2 9JT, United Kingdom 
References:
[1] 
M. I. Freidlin, Fluctuations in dynamical systems with averaging, Dok. Acad. Nauk SSSR, 226 (1976), 273276 (in Russian). Google Scholar 
[2] 
M. I. Freidlin, Averaging principle and large deviations, Uspekhi Matem. Nauk, 33 (1978) 107160. (in Russian). Google Scholar 
[3] 
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' SpringerVerlag, New York, 1984. Google Scholar 
[4] 
O. V. Gulinsky and A. Yu. Veretennikov, "Large Deviations for DiscreteTime Processes with Averaging,'' VSP, Utrecht, 1993. Google Scholar 
[5] 
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes,'' $2^{nd}$ edition, NorthHolland, Amsterdam, 1989. Google Scholar 
[6] 
T. Kato, "Perturbation Theory for Linear Operators,'' $2^{nd}$ edition, SpringerVerlag, New York, 1976. Google Scholar 
[7] 
Yu. Kifer, "Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging,'' Memoirs of the Amer. Math. Soc. 944, AMS, Providence, RI, 2009. Google Scholar 
[8] 
M. A. Krasnosel'skii, E. A. Lifshitz and A. V. Sobolev, "Positive Linear Systems,'' Helderman, Berlin, 1989. Google Scholar 
[9] 
N. V. Krylov, "Introduction to the Theory of Random Processes,'' AMS, Providence, RI, 1995. Google Scholar 
[10] 
R. S. Liptser, Large deviations for two scaled diffusions, Probability Theory and Related Fields, 106(1) (1996), 71104; preprint version (2005) at arXiv:math/0510029. Google Scholar 
[11] 
R. Liptser, V. Spokoiny and A. Yu. Veretennikov, FreidlinWentzell type large deviations for smooth processes, Markov Processes and Related Fields, 8 (2002), 611636. Google Scholar 
[12] 
R. T. Rockafellar, "Convex Analysis,'' Princeton Univ. Press., Princeton, NJ, 1970. Google Scholar 
[13] 
A. Yu. Veretennikov, On large deviations in the averaging principle for stochastic differential equations with periodic coefficients 2, Math. USSR Izvestiya, 39 (1992), 677701. Google Scholar 
[14] 
A. Yu. Veretennikov, Large deviations in averaging principle for stochastic differential equation systems (noncompact case), Stochastics Stochastics Rep., 48 (1994), 8396. Google Scholar 
[15] 
A. Yu. Veretennikov, On large deviations for stochastic differential equations with a small diffusion and averaging, Theory Probab. Appl., 43 (1998), 335337. Google Scholar 
[16] 
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', Ann. Probab., 27(1) (1999) 284296. Google Scholar 
[17] 
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', correction,, preprint, (). Google Scholar 
show all references
References:
[1] 
M. I. Freidlin, Fluctuations in dynamical systems with averaging, Dok. Acad. Nauk SSSR, 226 (1976), 273276 (in Russian). Google Scholar 
[2] 
M. I. Freidlin, Averaging principle and large deviations, Uspekhi Matem. Nauk, 33 (1978) 107160. (in Russian). Google Scholar 
[3] 
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' SpringerVerlag, New York, 1984. Google Scholar 
[4] 
O. V. Gulinsky and A. Yu. Veretennikov, "Large Deviations for DiscreteTime Processes with Averaging,'' VSP, Utrecht, 1993. Google Scholar 
[5] 
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes,'' $2^{nd}$ edition, NorthHolland, Amsterdam, 1989. Google Scholar 
[6] 
T. Kato, "Perturbation Theory for Linear Operators,'' $2^{nd}$ edition, SpringerVerlag, New York, 1976. Google Scholar 
[7] 
Yu. Kifer, "Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging,'' Memoirs of the Amer. Math. Soc. 944, AMS, Providence, RI, 2009. Google Scholar 
[8] 
M. A. Krasnosel'skii, E. A. Lifshitz and A. V. Sobolev, "Positive Linear Systems,'' Helderman, Berlin, 1989. Google Scholar 
[9] 
N. V. Krylov, "Introduction to the Theory of Random Processes,'' AMS, Providence, RI, 1995. Google Scholar 
[10] 
R. S. Liptser, Large deviations for two scaled diffusions, Probability Theory and Related Fields, 106(1) (1996), 71104; preprint version (2005) at arXiv:math/0510029. Google Scholar 
[11] 
R. Liptser, V. Spokoiny and A. Yu. Veretennikov, FreidlinWentzell type large deviations for smooth processes, Markov Processes and Related Fields, 8 (2002), 611636. Google Scholar 
[12] 
R. T. Rockafellar, "Convex Analysis,'' Princeton Univ. Press., Princeton, NJ, 1970. Google Scholar 
[13] 
A. Yu. Veretennikov, On large deviations in the averaging principle for stochastic differential equations with periodic coefficients 2, Math. USSR Izvestiya, 39 (1992), 677701. Google Scholar 
[14] 
A. Yu. Veretennikov, Large deviations in averaging principle for stochastic differential equation systems (noncompact case), Stochastics Stochastics Rep., 48 (1994), 8396. Google Scholar 
[15] 
A. Yu. Veretennikov, On large deviations for stochastic differential equations with a small diffusion and averaging, Theory Probab. Appl., 43 (1998), 335337. Google Scholar 
[16] 
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', Ann. Probab., 27(1) (1999) 284296. Google Scholar 
[17] 
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', correction,, preprint, (). Google Scholar 
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