# Power, Levy, Exponential and Gaussian Regimes in Autocatalytic Financial Systems

## Author Info

• Zhi-Feng Huang
• Sorin Solomon

## 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 $\alpha$ 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

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File URL: http://arxiv.org/pdf/cond-mat/0008026

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/0008026.

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 Length: Date of creation: Aug 2000 Date of revision: Publication status: Published in Eur. Phys. J. B 20 (2001) 601-607 Handle: RePEc:arx:papers:cond-mat/0008026 Contact details of provider: Web page: http://arxiv.org/

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