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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), 273-276 (in Russian). |
| [2] |
M. I. Freidlin, Averaging principle and large deviations, Uspekhi Matem. Nauk, 33 (1978) 107-160. (in Russian). |
| [3] |
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' Springer-Verlag, New York, 1984. |
| [4] |
O. V. Gulinsky and A. Yu. Veretennikov, "Large Deviations for Discrete-Time Processes with Averaging,'' VSP, Utrecht, 1993. |
| [5] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes,'' $2^{nd}$ edition, North-Holland, Amsterdam, 1989. |
| [6] |
T. Kato, "Perturbation Theory for Linear Operators,'' $2^{nd}$ edition, Springer-Verlag, New York, 1976. |
| [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. |
| [8] |
M. A. Krasnosel'skii, E. A. Lifshitz and A. V. Sobolev, "Positive Linear Systems,'' Helderman, Berlin, 1989. |
| [9] |
N. V. Krylov, "Introduction to the Theory of Random Processes,'' AMS, Providence, RI, 1995. |
| [10] |
R. S. Liptser, Large deviations for two scaled diffusions, Probability Theory and Related Fields, 106(1) (1996), 71-104; preprint version (2005) at arXiv:math/0510029. |
| [11] |
R. Liptser, V. Spokoiny and A. Yu. Veretennikov, Freidlin-Wentzell type large deviations for smooth processes, Markov Processes and Related Fields, 8 (2002), 611-636. |
| [12] |
R. T. Rockafellar, "Convex Analysis,'' Princeton Univ. Press., Princeton, NJ, 1970. |
| [13] |
A. Yu. Veretennikov, On large deviations in the averaging principle for stochastic differential equations with periodic coefficients 2, Math. USSR Izvestiya, 39 (1992), 677-701. |
| [14] |
A. Yu. Veretennikov, Large deviations in averaging principle for stochastic differential equation systems (noncompact case), Stochastics Stochastics Rep., 48 (1994), 83-96. |
| [15] |
A. Yu. Veretennikov, On large deviations for stochastic differential equations with a small diffusion and averaging, Theory Probab. Appl., 43 (1998), 335-337. |
| [16] |
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', Ann. Probab., 27(1) (1999) 284-296. |
| [17] |
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', correction, preprint, arXiv:math/0502098 [math.PR] \textbf{} (2005/2012). |
show all references
References:
| [1] |
M. I. Freidlin, Fluctuations in dynamical systems with averaging, Dok. Acad. Nauk SSSR, 226 (1976), 273-276 (in Russian). |
| [2] |
M. I. Freidlin, Averaging principle and large deviations, Uspekhi Matem. Nauk, 33 (1978) 107-160. (in Russian). |
| [3] |
M. I. Freidlin and A. D. Wentzell, "Random Perturbations of Dynamical Systems,'' Springer-Verlag, New York, 1984. |
| [4] |
O. V. Gulinsky and A. Yu. Veretennikov, "Large Deviations for Discrete-Time Processes with Averaging,'' VSP, Utrecht, 1993. |
| [5] |
N. Ikeda and S. Watanabe, "Stochastic Differential Equations and Diffusion Processes,'' $2^{nd}$ edition, North-Holland, Amsterdam, 1989. |
| [6] |
T. Kato, "Perturbation Theory for Linear Operators,'' $2^{nd}$ edition, Springer-Verlag, New York, 1976. |
| [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. |
| [8] |
M. A. Krasnosel'skii, E. A. Lifshitz and A. V. Sobolev, "Positive Linear Systems,'' Helderman, Berlin, 1989. |
| [9] |
N. V. Krylov, "Introduction to the Theory of Random Processes,'' AMS, Providence, RI, 1995. |
| [10] |
R. S. Liptser, Large deviations for two scaled diffusions, Probability Theory and Related Fields, 106(1) (1996), 71-104; preprint version (2005) at arXiv:math/0510029. |
| [11] |
R. Liptser, V. Spokoiny and A. Yu. Veretennikov, Freidlin-Wentzell type large deviations for smooth processes, Markov Processes and Related Fields, 8 (2002), 611-636. |
| [12] |
R. T. Rockafellar, "Convex Analysis,'' Princeton Univ. Press., Princeton, NJ, 1970. |
| [13] |
A. Yu. Veretennikov, On large deviations in the averaging principle for stochastic differential equations with periodic coefficients 2, Math. USSR Izvestiya, 39 (1992), 677-701. |
| [14] |
A. Yu. Veretennikov, Large deviations in averaging principle for stochastic differential equation systems (noncompact case), Stochastics Stochastics Rep., 48 (1994), 83-96. |
| [15] |
A. Yu. Veretennikov, On large deviations for stochastic differential equations with a small diffusion and averaging, Theory Probab. Appl., 43 (1998), 335-337. |
| [16] |
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', Ann. Probab., 27(1) (1999) 284-296. |
| [17] |
A. Yu. Veretennikov, On large deviations in the averaging principle for SDE's with a "full dependence'', correction, preprint, arXiv:math/0502098 [math.PR] \textbf{} (2005/2012). |
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