Zero-one-only process: a correlated random walk with a stochastic   ratchet
  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. 
Seung Ki Baek, Hawoong Jeong, Seung-Woo Son, Beom Jun Kim
physics.data-an cond-mat.stat-mech