NOVEL PERTURBATION EXPANSION FOR THE LANGEVIN EQUATION

We discuss the randomly driven system dx/dt = -W(x) + f(t), where f(t) is a Gaussian random function or stirring force with <f(t) f(t')> = 2-delta-(t-t'), and W(x) is of the form gx1 + 2-delta. The parameter delta is a measure of the nonlinearity of the equation. We show how to obtain the correlation functions <x(t) x(t')... x(t(n))>f as a power series in delta. We obtain three terms in the delta expansion and show how to use Pade approximants to analytically continue the answer in the variable delta. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for all g and delta.