NATURE OF THE RANDOM FORCE IN BROWNIAN-MOTION

We study the stochastic properties of the random force in a nonlinear Langevin equation for the time dependence of a variable alpha whose equilibrium distribution function P(eq)(alpha) is known. We assume that this random force is of a multiplicative character and consists of a factor C(alpha(t - epsilon)) multiplied by a random function f0(t) independent of alpha(t). We prove that in this case f0(t) is a Gaussian white process. We show that the function C(alpha) is the solution of a differential equation which involves P(eq)(alpha) and can easily be solved when this last function is Gaussian.