Invariant power law distribution of langevin systems with colored multiplicative noise
The random multiplicative process is studied for the case of a colored multiplicative noise with exponentially decreasing autocorrelation function. We observe the power law exponent of probability distribution in a statistically steady state numerically to clarify the effect of finite correlation time. The renormalization procedure is applied to derive the power law exponent theoretically. The power law exponent is inversely proportional to the autocorrelation time of the multiplicative noise.
Sato
AH
Research Institute of Electrical Communication, Tohoku University, Sendai 980-8577, Japan.
Takayasu
H
Sawada
Y