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<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.
Continuous-time random walk between Lévy-spaced targets in the real line / Bianchi A.; Lenci M.; Pene F.. - In: STOCHASTIC PROCESSES AND THEIR APPLICATIONS. - ISSN 0304-4149. - STAMPA. - 130:2(2020), pp. 708-732. [10.1016/j.spa.2019.03.010]
Continuous-time random walk between Lévy-spaced targets in the real line
Lenci M.;
2020
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<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.File | Dimensione | Formato | |
---|---|---|---|
spa2019-130-2.pdf
Open Access dal 23/03/2021
Tipo:
Postprint
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
499.2 kB
Formato
Adobe PDF
|
499.2 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.