Anomalous statistics in turbulence, financial markets and other complex systems
Article first published online: 14 JUN 2004
Copyright © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 13, Issue 7-8, pages 450–460, July 2004
How to Cite
Peinke, J., Böttcher, F. and Barth, St. (2004), Anomalous statistics in turbulence, financial markets and other complex systems. Ann. Phys., 13: 450–460. doi: 10.1002/andp.200410088
- Issue published online: 14 JUN 2004
- Article first published online: 14 JUN 2004
- Manuscript Accepted: 5 APR 2004
- Manuscript Received: 3 FEB 2004
- Stochastic processes;
- random walks and Levy flights;
- isotropic turbulence.
The meaning of non-Gaussian statistics of disordered systems is discussed. The risks of heavy tailed probability distributions of wind gusts are presented together with the discussion of an eventual power law behavior of such heavy tailed distributions. We summarize the argumentation connecting such probability distributions with Levy processes and the meaning of non-existing moments. Based on turbulence and financial market data, stochastic cascade processes are presented, which lead to anomalous statistics with heavy tails, too. Finally we show how for disordered complex systems with an underlying hierarchical structure, like the cascade structure in turbulence, a stochastic equation can be estimated directly from the data. The numerical solution of this reconstructed stochastic process gives back the anomalous statistics.