Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles

Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling
##IMG## [http://ej.iop.org/images/1751-8121/52/9/095601/aaafe90ieqn001.gif] with ##IMG##
[http://ej.iop.org/images/1751-8121/52/9/095601/aaafe90ieqn002.gif] in the probability density
function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian
motion, and power-law decaying distributions, e.g. Lévy Flights or Lévy Walks (LWs). Lévy flights
get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite
position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping
events, overcome these limitations: they resemble a Lévy-type power-law distribution that is
truncated in the large displacement range and have finite moments, finite energy and, even with
discontinuous velocity, they are continuous. However, LWs do not take into acco...

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