  We study the limiting behaviors of a generalized elephant random walk on the
integer lattice. This random walk is defined by using two sequences of
parameters expressing the memory at each step from the whole past and the drift
of each step to the right, respectively. This model is also regarded as a
dependent Bernoulli process. Our results reveal how the scaling factors are
determined by the behaviors of the parameters. In particular, we allow the
degeneracy of the parameters. We further present several examples in which the
scaling factors are explicitly computed.
