One class of universal mechanisms that generate power-law probability distributions is that of random multiplicative processes. In this paper, we consider a multiplicative Langevin equation driven by non-Gaussian colored multipliers. We analytically derive a formula that relates the power-law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two-valued Markov process. We also investigate the relationship between our treatment and the large deviation analysis of time series, and demonstrate the appearance of log-periodic fluctuations superimposed on the power-law distribution due to the non-Gaussian nature of the multipliers. © 2006 Elsevier B.V. All rights reserved.
CITATION STYLE
Kitada, S. (2006). Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers. Physica A: Statistical Mechanics and Its Applications, 370(2), 539–552. https://doi.org/10.1016/j.physa.2006.02.039
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