Power-Law Tails from Multiplicative Noise
Power-Law Tails from Multiplicative Noise
We show that the well-known linear Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution for sufficiently large momenta. At finite ratio of the correlation …