Power-law Exponent in Multiplicative Langevin Equation with Temporally Correlated Noise

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 systems, 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.

Genetic noise mechanism for power-law switching in bacterial flagellar motors

“…time in the height of these barriers can produce an algebraic scaling in the distribution of CCW durations [15]. These studies are in line with a broader research trend aimed at understanding of the genesis of power-law distributions in Langevin systems with multiplicative nosie [16][17][18]. However, the origin of such fluctuations was not well-established in Ref.…”