Langevin equation with scale-dependent noise

The Langevin equation dφ (t,x)/dt = U[φ(t,x)] + η(t,x) is one of the most general approximations for a large variety of physical, chemical, biological and other systems with fluctuating environment. The common way to solve the Langevin equation is the stochastic perturbative expansion in a small interaction parameter with the averaging over the Gaussian random force η (t,x) in each order of the perturbation expansion. This approach leads to the divergences, similar to those in quantum field theory, and requires the application of renormalization group methods. A perturbation theory based on wavelet transform is proposed. It is shown, that for a limited band forcing, the proposed technique leads directly to a finite result and does not require renormalization