Levy walks with rests: Long-time analysis

In this paper we analyze the asymptotic behavior of Levy 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 Levy walk or the process describing competition between subdiffusion and Levy flights. Some other more complicated limit forms are also possible to obtain. Finally we present some numerical results, which confirm our findings.