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Continuous-time random walk between Lévy-spaced targets in the real line

Author

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  • Bianchi, Alessandra
  • Lenci, Marco
  • Pène, Françoise

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.

Suggested Citation

  • Bianchi, Alessandra & Lenci, Marco & Pène, Françoise, 2020. "Continuous-time random walk between Lévy-spaced targets in the real line," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 708-732.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:708-732
    DOI: 10.1016/j.spa.2019.03.010
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