Irina A. Kachanova, Sergey Y. Makhno
September 4, 2012
Abstract. A large deviations principle for the backward stochastic differential equations connected with solutions of Itô equations with small diffusion and coefficients depending on a small parameter is proved. It is not required the existence of the limits of coefficients by tending small parameter to zero. The functions can have oscillation under the first variable. The uniform convergence on compacts of the solutions of the quasilinear parabolic equations of the second order with a small parameter by the higher derivative to the generalized solution of nonlinear equation with the partial derivatives of the first order are proved for the justification of this principle of large deviations.