.On large deviations of the moment of attaining far level by the random walk in a random environment

We prove local limit theorems on large deviations for the moment $T_n$ of attaining the level $n\in\mathbb{N}$ by the random walk in a random environment. Exact asymptotics of probabilities ${\mathbf P}(T_n=k)$ are obtained for values of the parameter $k$ corresponding to the large deviations zone.