  We consider the problem of approximation of the solution of the backward
stochastic differential equation in the Markovian case. We suppose that the
trend coefficient of the diffusion process depends on some unknown parameter
and the diffusion coefficient of this equation is small. We propose an
approximation of this solution based on the one-step MLE of the unknown
parameter and we show that this approximation is asymptotically efficient in
the asymptotics of "small noise".
