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arXiv · 1709.05620

Power-law exponent in multiplicative Langevin equation with temporally correlated noise

Satoru Morita
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Abstract

Power-law distributions are ubiquitous in nature. Random multiplicative processes are a basic model for the generation of power-law distributions. It is known that, for discrete-time systems, the power-law exponent decreases as the autocorrelation time of the multiplier increases. However, for continuous-time ystems, it has not yet been elucidated as to how the temporal correlation affects the power-law behavior. Herein, we have analytically investigated a multiplicative Langevin equation with colored noise. We show that the power-law exponent depends on the details of the multiplicative noise, in contrast to the case of discrete-time systems.

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Satoru Morita. 2017-09-17. Power-law exponent in multiplicative Langevin equation with temporally correlated noise. https://doi.org/10.7566/jpsj.87.053801

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