Abstract <p>We suggest a simple generalization of Chapman–Kolmogorov equation used to describe many stochastic Markov processes in natural sciences. This generalization is based on the consideration that a random walker slips before reaching his next step. We discuss two exactly solvable cases. First, the bidirectional random walk with a slip which leads to familiar Ornstein–Uhlenbeck process. Second, unidirectional random walk with a slip, an unexplored area to the best of our knowledge. We show interesting pulse-like spatio-temporal evolution without spreading for this stochastic process in the long wavelength limit.</p> Graphical abstract <p></p>