Multidimensional Lévy walk and its scaling limits

In this paper we obtain the scaling limit of a multidimensional Lévy walk and describe the detailed structure of the limiting process. The scaling limit is a subordinated α-stable Lévy motion with the parent process and subordinator being strongly dependent processes. The corresponding Langevin pict...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-09, Vol.45 (38), p.385002-16
Main Authors: Teuerle, Marek, ebrowski, Piotr, Magdziarz, Marcin
Format: Article
Language:English
Subjects:
Constraining
Control equipment
convergence in distribution
Exact sciences and technology
Lévy walk
Mathematical models
Parents
Physics
Pictures
scaling limit
Simulation
Spectra
spectral measure
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Summary:In this paper we obtain the scaling limit of a multidimensional Lévy walk and describe the detailed structure of the limiting process. The scaling limit is a subordinated α-stable Lévy motion with the parent process and subordinator being strongly dependent processes. The corresponding Langevin picture is derived. We also introduce a useful method of simulating Lévy walks with a predefined spectral measure, which controls the direction of each jump. Our approach can be applied in the analysis of real-life data-we are able to recover the spectral measure from the data and obtain the full characterization of a Lévy walk. We also give examples of some useful spectral measures, which cover a large class of possible scenarios in the modeling of real-life phenomena.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/38/385002