Should I stay or should I go? Zero-size jumps in random walks for L\'evy flights

Gianni Pagnini; Silvia Vitali

doi:10.1515/fca-2021-0007

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arXiv · 2103.06981

Should I stay or should I go? Zero-size jumps in random walks for L\'evy flights

Gianni Pagnini·Silvia Vitali

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Abstract

We study Markovian continuous-time random walk models for L\'evy 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 L\'evy-like motion for wild animals.

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Gianni Pagnini, Silvia Vitali. 2021-03-11. Should I stay or should I go? Zero-size jumps in random walks for L\'evy flights. https://doi.org/10.1515/fca-2021-0007

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