Abstract
Lévy walks are non-Markovian stochastic processes, whose explosion of space with time is faster than regular Brownian motion but slower than ballistic motion. More concretely, they correspond to a random walk process with jump distribution , where is a power law waiting-time distribution. In this paper, we first investigate the probability distribution functions of Lévy walks, then discuss their aging phenomena, forward waiting-time probability distribution and numerical implementations.
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