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 Tn of attaining the level n ∈ ℕ by the random walk in a random environment. Exact asymptotics of probabilities P(Tn = k) are obtained for values of the parameter k corresponding to the large deviations zone. [ABSTRACT FROM AUTHOR]