Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1999-10-26
Physics
Condensed Matter
Statistical Mechanics
7 pages, five figures. To appear in Europhysics Letters (2000)
Scientific paper
10.1209/epl/i2000-00540-7
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated L\'{e}vy distribution. For both (i) and (ii), we find that due to the correlations in the variance, the process ``dynamically'' generates power-law tails in the distributions, whose exponents can be controlled through the way the correlations in the variance are introduced. For (ii), we find that the process can extend a truncated distribution {\it beyond the truncation cutoff}, which leads to a crossover between a L\'{e}vy stable power law and the present ``dynamically-generated'' power law. We show that the process can explain the crossover behavior recently observed in the $S&P500$ stock index.
Chessa Alessandro
Ivanov Plamen Ch
Lee Youngki
Podobnik Boris
Stanley Eugene H.
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