Applying the stochastic formalism to the test scalar field in de Sitter spacetime, we study in more details the effective theory of their infrared modes described by a Langevin equation. It corresponds to the well-known model A in statistical physics. We use the formulation in terms of a one dimensional supersymmetric field theory. We compute the unequal time field correlator at large (superhorizon) time separations in a 1/N expansion at NLO and compare with existing quantum field theory computation. We then attempt to get a result for finite N using the non perturbative renormalization group on this one dimensional theory, going beyond the local potential approximation.