We study Markovian continuos-time random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The significance of this result is two-fold: i ) with regard to the probabilistic derivation of the fractional diffusion equation and also ii ) with regard to the concept of site fidelity in the framework of Lévy-like motion for wild animals.

中文翻译：

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我该留下还是该走？Lévy航班随机行走时零跳

我们研究了Lévy航班的Markovian连续时间随机游走模型，并给出了一个示例，其中当跳跃遵循零中为零的双峰幂律分布时，不能保证收敛到稳定密度。该结果的意义有两个方面：i）关于分数扩散方程的概率推导，以及ii）关于野生动物Lévy样运动框架中的位点保真度的概念。