 Continuous-time random walk between Lévy-spaced targets in the real lineAlessandra Bianchi, Marco Lenci and Françoise Pène Stochastic Processes and their Applications, 2020, vol. 130, issue 2, 708-732 Abstract: 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 α-stable distribution with 0<α<1. This is therefore an example of a random walk in a Lévy random medium. Specifically, it is a generalization of a process known in the physical literature as Lévy–Lorentz gas. We prove that the annealed version of the process is superdiffusive with scaling exponent 1∕(α+1) and identify the limiting process, which is not càdlàg. The proofs are based on the technique of Kesten and Spitzer for random walks in random scenery. Keywords: Lévy–Lorentz gas; Random walk on point process; Anomalous diffusion; Lévy random medium; Stable process; Random walk in random scenery (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:130:y:2020:i:2:p:708-732 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2019.03.010 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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