Superposition of chaotic process with convergence to Levy's stable law

Details Superposition of chaotic process with convergence to Levy's stable law Superposition of chaotic process with convergence to Levy's stable law

1997-11-26

arxiv.org/abs/chao-dyn/9711023v4

Physical Review E Vol.58(1998),pp.2644-2647.

Physics

Condensed Matter

Statistical Mechanics

RevTeX 8 pages, 2 color figures, notation simpified, reference added

Scientific paper

10.1103/PhysRevE.58.2644

We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed random variables obeying such chaotic process converge in density to Levy's stable laws in a full range of the index parameters. The theory related to the connection between deterministic chaos and non-Gaussian distributions gives us a systematic view of the purely mechanical generation of Levy's stable laws.

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