Multi-scaling properties of truncated Levy flights

Details Multi-scaling properties of truncated Levy flights Multi-scaling properties of truncated Levy flights

2000-02-02

arxiv.org/abs/cond-mat/0002027v1

Phys. Lett. A 266 (2000) 282

Physics

Condensed Matter

Statistical Mechanics

9 pages, 6 figures, accepted for publication in Phys. Lett. A

Scientific paper

10.1016/S0375-9601(00)00059-1

Multi-scaling properties of one-dimensional truncated Levy flights are studied. Due to the broken self-similarity of the distribution of jumps, they are expected to possess multi-scaling properties in contrast to the ordinary Levy flights. We argue this fact based on a smoothly truncated Levy distribution, and derive the functional form of the scaling exponents. Specifically, they exhibit bi-fractal behavior, which is the simplest case of multi-scaling.

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