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Published on: February 8, 2019
Lévy walks with rests: Long-time analysis
Marcin Magdziarz1, Wladyslaw Szczotka2
1Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
Abstract:
In this paper we analyze the asymptotic behavior of Lévy walks with rests. Applying recent results in the field of functional convergence of continuous-time random walks we find the corresponding limiting processes. Depending on the parameters of the model, we show that in the limit we can obtain standard Lévy walk or the process describing competition between subdiffusion and Lévy flights. Some other more complicated limit forms are also possible to obtain. Finally we present some numerical results, which confirm our findings.
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