Abstract
Complex systems with a high degree of disorder are tradition- ally analyzed by means of multiscaling behavior of a scale dependent mea- sure. Here we present a new analysis based on scale dependent nonlinear stochastic processes. With these processes a more complete characteriza- tion of the complexity is achieved, namely, instead of characterizing the statistics of the scale dependent disorder on different scales separately, the knowledge of a stochastic process provides the complete stochastic infor- mation of the simultaneous occurrence of different disordered structures on all scales. Furthermore, we show how to reconstruct from given data the equations governing the stochastic processes.
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Peinke, J., Renner, C., Friedrich, R. (2002). Turbulence and Financial Market Data Analyzed with Respect to Their Scale Dependent Complexity. In: Skjeltorp, A.T., Vicsek, T. (eds) Complexity from Microscopic to Macroscopic Scales: Coherence and Large Deviations. NATO Science Series, vol 63. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0419-0_9
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DOI: https://doi.org/10.1007/978-94-010-0419-0_9
Publisher Name: Springer, Dordrecht
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