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Random walk model with waiting times depending on the preceding jump length

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Citation

Zaburdaev, V. (2006). Random walk model with waiting times depending on the preceding jump length. Journal of Statistical Physics, 123(4), 871-881. doi:10.1007/s10955-006-9104-0.


Cite as: http://hdl.handle.net/21.11116/0000-0008-6180-9
Abstract
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.