Continuous-time random walk between L\'evy-spaced targets in the real line
| Autor: | Bianchi, Alessandra, Lenci, Marco, Pène, Françoise |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Stochastic Process. Appl. 130 (2020), no. 2, 708-732 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.spa.2019.03.010 |
| Popis: | We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal domain of attraction of an $\alpha$-stable distribution with $0 < \alpha < 1$. This is therefore an example of a random walk in a L\'evy random medium. Specifically, it is a generalization of a process known in the physical literature as L\'evy-Lorentz gas. We prove that the annealed version of the process is superdiffusive with scaling exponent $1/(\alpha + 1)$ and identify the limiting process, which is not c\`adl\`ag. The proofs are based on the technique of Kesten and Spitzer for random walks in random scenery. Comment: Final version to be published in Stochastic Processes and their Applications. 27 pages |
| Databáze: | arXiv |
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