Multidimensional Levy walk and its scaling limits

被引:27
作者
Teuerle, Marek [1 ]
Zebrowski, Piotr [2 ]
Magdziarz, Marcin [1 ]
机构
[1] Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, PL-50370 Wroclaw, Poland
[2] Univ Wroclaw, Math Inst, PL-50384 Wroclaw, Poland
关键词
DIFFUSION; FLIGHT; DISPERSION; TRANSPORT; EQUATIONS; THEOREMS; PATTERNS; MODELS; LAWS;
D O I
10.1088/1751-8113/45/38/385002
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we obtain the scaling limit of a multidimensional Levy walk and describe the detailed structure of the limiting process. 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 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 Levy 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.
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页数:16
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