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•We introduce a new model of fractional dynamics, which can be used to model Levy flights in static (quenched) environment. •We derive the long-time limit of the introduced process (functional convergence in the Skorokhod topology). •We show that the resulting limiting process displays scaling, which is typical for sub-, quasi- and superdiffusion regimes. •We analyze the asymptotic behavior of...
In this paper we derive Langevin picture of Lévy walks. Applying recent advances in the theory of coupled continuous time random walks we find a limiting process of the properly scaled Lévy walk. Next, we introduce extensions of Levy walks, in which jump sizes are some functions of waiting times. We prove that under proper scaling conditions, such generalized Lévy walks converge in distribution to...
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