https://doi.org/10.1007/PL00011114
Power, Lévy, exponential and Gaussian-like regimes in autocatalytic financial systems
1
Institute for Theoretical Physics, Cologne University, 50923 Köln, Germany
2
Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel
Corresponding author: a zfh@physics.utoronto.ca
Received:
29
July
2000
Revised:
25
September
2000
Published online: 15 April 2001
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 
, the power law decay with large
exponent (
), 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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
