Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-08-02
Eur. Phys. J. B 20 (2001) 601-607
Physics
Condensed Matter
Statistical Mechanics
9 pages with 5 figures; Proceedings of EPS conference "Applications of Physics in Financial Analysis 2", 13 to 15 July 2000 Li
Scientific paper
10.1007/PL00011114
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 $\alpha$ 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 Levy regime $\alpha < 2$, the power law decay with large exponent ($\alpha > 2$), 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.
Huang Zhi-Feng
Solomon Sorin
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