  The investigation of random walks is central to a variety of stochastic
processes in physics, chemistry, and biology. To describe a transport
phenomenon, we study a variant of the one-dimensional persistent random walk,
which we call a zero-one-only process. It makes a step in the same direction as
the previous step with probability $p$, and stops to change the direction with
$1-p$. By using the generating-function method, we calculate its characteristic
quantities such as the statistical moments and probability of the first return.
