Systems with correlations in the variance: Generating power law tails in probability distributions

We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with co rrelations in the variance generated by i) a Gaussian or ii) a truncated Le 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 corre lations in the variance are introduced. For ii), we find that the process c an extend a truncated distribution beyond the truncation cutoff, which lead s to a crossover between a Levy stable power law and the present "dynamical ly generated" power law. We show that the process can explain the crossover behavior recently observed in the S&P500 stock index.