  We show that the occurrence of chaotic diffusion in a typical class of
time-delayed systems with linear instantaneous and nonlinear delayed term can
be well described by an anti-persistent random walk. We numerically investigate
the dependence of all relevant quantities characterizing the random walk on the
strength of the nonlinearity and on the delay. With the help of analytical
considerations, we show that for a decreasing nonlinearity parameter the
resulting dependence of the diffusion coefficient is well described by Markov
processes of increasing order.
