1. The problem statement, all variables and given/known data [tex] (\partial_t - A\nabla^2 + B)f(x) = \eta(x, t) [/tex] So I have a homogeneous linear differential equation except for an added noise term ##\eta(t) ##. The noise is uncorrelated between times and has a Gaussian distribution with zero mean. That is we have Gaussian white noise. The problem is to calculate the time dependence of f(x,t) and also the time dependence of ##\left| F(k, t)\right|^2 ##, where F(k, t) is the Fourier transform of f(x, t). 2. Relevant equations 3. The attempt at a solution If I know the specific function for the noise, I can solve using the Green's function - but I do not know ##\eta(t) ##. What can I say about the behavior of the solution? If you like, the noise starts at t=0, and we are interested in some kind of transient response I suppose. I began to proceed with solving the Green's function in Fourier space (that is x -> k, but t remained unchanged) but I am not sure what to do next. I am wishing I knew or remember more I guess.