  In continuum one-dimensional space, a coupled directed continuous time random
walk model is proposed, where the random walker jumps toward one direction and
the waiting time between jumps affects the subsequent jump. In the proposed
model, the Laplace-Laplace transform of the probability density function
$P(x,t)$ of finding the walker at position $x$ at time $t$ is completely
determined by the Laplace transform of the probability density function
$\varphi(t)$ of the waiting time. In terms of the probability density function
of the waiting time in the Laplace domain, the limit distribution of the random
process and the corresponding evolving equations are derived.
