  In this paper we continue our study of exit times for random walks with
independent but not necessarily identical distributed increments. Our paper
"First-passage times for random walks with non-identically distributed
increments" was devoted to the case when the random walk is constructed by a
fixed sequence of independent random variables which satisfies the classical
Lindeberg condition. Now we consider a more general situation when we have a
triangular array of independent random variables. Our main assumption is that
the entries of every row are uniformly bounded by a constant, which tends to
zero as the number of the row increases.
