Dynamical Systems That Produce the Levy Flights.

Miyaguchi Tomoshige, Aizawa Yoji

doi:10.1143/ptp.106.697

Dynamical Systems That Produce the Levy Flights.

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Miyaguchi Tomoshige

Department of Applied Physics, Faculty of Science and Engineering Waseda University, Tokyo 169-8555, Japan
Aizawa Yoji

Department of Applied Physics, Faculty of Science and Engineering Waseda University, Tokyo 169-8555, Japan

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説明

We introduce a one-dimensional map producing flights of arbitrary length and explain that the orbits and the density functions that evolve under this map have the same properties as Lévy flight. We derive an approximated Frobenius-Perron equation and prove that this equation converges to the Lévy diffusion equation.