The exact distribution of a simple correlated walk with a stationary initial condition

The exact distribution probabilities and the mean square displacements are derived for a simple one-dimensional correlated walk with an initial condit ion which is stationary and direction-independent. The mean square displace ments are independent of the initial condition, as expected. The existence of the runaway component is shown to be the result of a correlation between the steps themselves. After infinite time, the runaway component is absorb ed by the diffusive component, but the degree of correlation is unity. The absorbed time depends on the degree of the correlation.