Limit theorems for asymmetric random walk

The paper deals with an asymmetric random walk with transition probabilities $p_{k,k+1}=p$, $p_{k,k-1}=1-p=q<p$. Let $S_k$ be the location of the system at time $k$; $f(k)$ be a function determined for all integers $k$. For some class of functions $f$ the limit behavior as $p-q\to0$ of the functionals of the type $\sum_{k=0}^\infty f(S_k)$ is studied.