Evolution in a Gaussian random field

We consider an evolution process in a Gaussian random field V(q) with the mean <V(q)> = 0 and the correlation function W (\q - q'\) equivalent to <V (q) V (q')>, where q epsilon R-d and d is the dimension of the Euclidean space R-d. For the value <G(q, t; q(0))>, t > 0, of the Green's function of the evolution equation averaged over all realizations of the random field, we use the Feynman-Kac formula to establish an integral equation that is invariant with respect to a continuous renormalization group. This invariance property allows using the renormalization group method to find an asymptotic expression for <G(q, t; q(0))> as \q - q(0)\ --> infinity and t --> infinity.