The holographic RG of Anti-De Sitter gives a powerful clue about theunderlying AdS/CFT correspondence.The question is whether similar hints can be found for the heretoforeelusive holographic dual of De Sitter.The framework of stochastic inflation uses a nonperturbative insightin order to tame bad behavior in theperturbation series at late times. Recasting this as a "resummationof time", we wish understand whetherthe distributions that result can be thought of as an attractive UVfixed point of a theory living on a spacelikeslice of DS. I will discuss our rederivation of stochastic inflationin terms of wavefunctionals, the straightforwardway one can implement corrections to the leading approximations, andthe robustness of the late-time equilibriumto perturbations.