论文信息 - On large deviations in the averaging principle for SDE's with a "full dependence,'' revisited - 字舞流文

On large deviations in the averaging principle for SDE's with a "full dependence,'' revisited

We establish a large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one, including diffusion.

Alexander Yu. Veretennikov

[1] Tosio Kato. Perturbation theory for linear operators , 1966 .

[2] Vladimir Spokoiny,et al. Freidlin-Wentzell type large deviations for smooth processes , 2002 .

[3] ON LARGE DEVIATIONS IN THE AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS. II , 1992 .

[4] N. Krylov,et al. Introduction to the Theory of Random Processes , 2002 .

[5] L. Rogers. Stochastic differential equations and diffusion processes: Nobuyuki Ikeda and Shinzo Watanabe North-Holland, Amsterdam, 1981, xiv + 464 pages, Dfl.175.00 , 1982 .

[6] Yuri Kifer,et al. Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging , 2007, 0710.2405.

[7] On Large Deviations for Stochastic DifferentialEquations with a Small Diffusion and Averaging , 1999 .

[8] A. Veretennikov,et al. Large Deviations for Discrete-Time Processes with Averaging , 1993 .

[9] M. Freidlin,et al. Random Perturbations of Dynamical Systems , 1984 .

[10] R. Liptser. Large deviations for two scaled diffusions , 1996 .

[11] Large deviations in averaging principle for stochastic differential equation systems (noncompact case) , 1994 .