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

A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time