Continuous Markovian model for Levy random walks with superdiffusive and superballistic regimes

Abstract

We consider a previously devised model describing Levy random walks (Phys. Rev E 79, 011110; 80, 031148, (2009)). It is demonstrated numerically that the given model describes Levy random walks with superdiffusive, ballistic, as well as superballistic dynamics. Previously only the superdiffusive regime has been analyzed. In this model the walker velocity is governed by a nonlinear Langevin equation. Analyzing the crossover from small to large time scales we find the time scales on which the velocity correlations decay and the walker motion essentially exhibits Levy statistics. Our analysis is based on the analysis of the geometric means of walker displacements and allows us to tackle probability density functions with power-law tails and, correspondingly, divergent moments.

10 pages, 2 figures

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Cited by in corpus (3)

• Onset of anomalous diffusion from local motion rules
• Truncated Levy Random Walks and Generalized Cauchy Processes
• Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle