Random walk model with waiting times depending on the preceding jump length - Zaburdaev, Vasily (Journal of Statistical Physics, 2006)
In the present paper, the generalized continuous time random walk model with a coupled transition kernel is considered. The coupling occurs through the dependence of the waiting time probability distribution on the preceding jump length. For the description of this model, a method is suggested that includes the details of the microscopic distribution over the waiting times and arrival distances at a given point. A close analogy to the problem of a random walk with finite velocity is demonstrated for the particular case of coupling, when a waiting time is a simple function of a preceding jump length. With its help an analytical solution for the generalized random walk model is found, including both effects (finite velocity and jump dependent waiting times) simultaneously. © 2006 Springer Science+Business Media, Inc.
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Keywords: Continuous time random walk model; Coupled transition kernel; Fractional derivatives; Green's function; Levy flights