Multidimensional Levy walk and its scaling limits

Marek Teuerle, Piotr Zebrowski and Marcin Magdziarz

No HSC/11/06, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

Abstract: In this paper we obtain the scaling limit of multidimensional Levy walk and describe the detailed structure of the limiting process. It occurs that the scaling limit is a subordinated alpha-stable Levy 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 Levy walks with 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 Levy walk. We also give examples of some useful spectral measures, which cover large class of possible scenarios in the modeling of real-life phenomena.

Keywords: Levy walk; scaling limit; convergence in distribution; spectral measure (search for similar items in EconPapers)
JEL-codes: C33 C46 C53 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in J. Phys A: Math. Theor 45, 385002 (2012).

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http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_11_06.pdf Original version, 2011 (application/pdf)

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