Abstract
Although the second displacement moments for Lévy flights are not defined in their usual sense, a few years ago it was shown that nonextensive statistical mechanics can be used to define them for symmetric flights. Here it is shown that the displacement moments for long-jump asymmetric Lévy flights can also be regularized by calculating the averages in the form prescribed by nonextensive statistical mechanics. The dependence of the generalized diffusion coefficient on the asymmetry strength is investigated. It is also shown that no extremum q -entropy principle can be associated with the asymmetric Lévy attractors.
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