Should i stay or should i go? zero-size jumps in random walks for lévy flights-Reference-Cited by-同舟云学术

Should i stay or should i go? zero-size jumps in random walks for lévy flights

Published:2021-01-29 Issue:1 Volume:24 Page:137-167
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Pagnini Gianni¹²,Vitali Silvia¹

Affiliation:

1. BCAM - Basque Center for Applied Mathematics, Alameda Mazarredo , 14, 48009 , Bilbao , Basque Country , Spain

2. Ikerbasque - Basque Foundation for Science, Euskadi Plaza , 5, 48009 , Bilbao , Basque Country , Spain

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2021-0007/pdf

Reference72 articles.

1. E. Affili, S. Dipierro, E. Valdinoci, Decay estimates in time for classical and anomalous diffusion. In: 2018 MATRIX Annals (D. Wood, J. de Gier, C. Praeger, T. Tao, Eds.), MATRIX Book Series, Vol. 3, Springer, Cham (2020), 167–182.

2. E. Barkai, CTRW pathways to the fractional diffusion equation. Chem. Phys. 284, No 1-2 (2002), 13–27.

3. S. Benhamou, How many animals really do the Lévy walk? Ecology88, No 8 (2007), 1962–1969.

4. S. Benhamou, J. Collet, Ultimate failure of the Lévy foraging hypothesis: two-scale searching strategies outperform scale-free ones even when prey are scarce and cryptic. J. Theor. Biol. 387 (2015), 221–227.

5. G. Berthelot, S. Saïd, V. Bansaye, How to use random walks for modeling the movement of wild animals. bioRxiv Preprint (2020); 10.1101/2020.03.11.986885.

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