Lower bound for large deviations for an averaged SDE with a small diffusion (Q1267459)

Large deviations of a singularly perturbed stochastic differential system driven by a two-dimensional Wiener process are studied. The author proves a representation of the rate function \(S(\varphi)\) which occurs in the large deviation problem of finding lower bounds in the Freidlin-Wentzell form [see \textit{M. I. Frejdlin} and \textit{A. D. Venttsel'}, ``Random perturbations of dynamical systems'' (1984; Zbl 0522.60055)]. Another approach to the presented problem and representation of rate function is given by \textit{R. Liptser} [Probab. Theory Relat. Fields 106, No. 1, 71-104 (1996; Zbl 0855.60030)].