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

Shuya Kitada

Physica A: Statistical Mechanics and its Applications, 2006, vol. 370, issue 2, 539-552

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.

Keywords: Random multiplicative process; Power-law distribution; Non-Gaussian colored noise (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:370:y:2006:i:2:p:539-552

DOI: 10.1016/j.physa.2006.02.039

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