Martingale methods for random walks in a one-dimensional random environment

One-dimensional random walk processes in a random environment of a general functional type are considered. The study is carried out by the natural scale method. We obtain conditions of existence of the natural scale, conditions of existence of the processes and a theorem on the representation of the local time as the compensator of the modulus of the martingale which is the random walk in the natural scale. The work is performed in martingale terms and contains a number of examples.