  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.
