A criterion for linear drift, and the central limit theorem for one-dimensional random walks in a random environment

A study is made of one-dimensional random walks in a random environment with bounded jumps in a unit of time (no more than $L$ to the left and no more than $R$ to the right, where $R$ and $L$ are positive integers). A criterion for linear drift is proved, along with the central limit theorem for such random walks in a random environment.