Should I stay or should I go? Zero-size jumps in random walks for Lévy flights

Abstract

We study Markovian continuous-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.

References in corpus (4)

• Lévy walks
• Random walks with preferential relocations to places visited in the past and their application to biology
• First-passage and first-hitting times of Levy flights and Levy walks
• Subordination Pathways to Fractional Diffusion

Cited by in corpus (4)

• Anomalous diffusion originated by two Markovian hopping-trap mechanisms
• Choquard equation involving mixed local and nonlocal operators
• Normalized solutions to a Choquard equation involving mixed local and nonlocal operators
• Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators