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Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers

Author

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  • Kitada, Shuya

Abstract

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.

Suggested Citation

  • Kitada, Shuya, 2006. "Power-law distributions in random multiplicative processes with non-Gaussian colored multipliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 539-552.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:539-552
    DOI: 10.1016/j.physa.2006.02.039
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