Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions
Abstract
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.
Keywords
Cite
@article{arxiv.cond-mat/9910433,
title = {Systems with Correlations in the Variance: Generating Power-Law Tails in Probability Distributions},
author = {Boris Podobnik and Plamen Ch. Ivanov and Youngki Lee and Alessandro Chessa and H. Eugene Stanley},
journal= {arXiv preprint arXiv:cond-mat/9910433},
year = {2009}
}
Comments
7 pages, five figures. To appear in Europhysics Letters (2000)