Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems

Z.F. Huang and S. Solomon
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Z.F. Huang: Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany
S. Solomon: Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel

The European Physical Journal B: Condensed Matter and Complex Systems, 2001, vol. 20, issue 4, 601-607

Abstract: Abstract: We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents α of these power laws are time independent and depend only on the way the elements with very small values are treated. These truncated power laws determine the collective time evolution of the system. In particular the global stochastic fluctuations of the system differ from the normal Gaussian noise according to the time and size scales at which these fluctuations are considered. We describe the ranges in which these fluctuations are parameterized respectively by: the Lévy regime α 2), and the exponential decay. Finally we relate these results to the large exponent power laws found in the actual behavior of the stock markets and to the exponential cut-off detected in certain recent measurement.

Keywords: PACS. 05.40.+j Fluctuation phenomena; random processes; noise; and Brownian motion – 05.70.Ln Nonequilibrium and irreversible thermodynamics – 02.50.-r Probability theory; stochastic processes; and statistics (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/PL00011114

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