De Sitter Wavefunctionals and the Resummation of Time

The holographic RG of Anti-De Sitter gives a powerful clue about the underlying AdS/CFT correspondence.  The question is whether similar hints can be found for the heretofore elusive holographic dual of De Sitter. The framework of stochastic inflation uses nonperturbative insight to tame bad behavior in the  perturbation series of a massless scalar in DS at late times.  Remarkably, this fully quantum system loses phase information in the leading approximation, but retains a probabilistic character and allows for a controlled  prediction of late time Green's functions.  Recasting this as a "resummation of time", we wish 
understand whether the distributions that result can be thought of as an attractive UV fixed point of a theory  living on a spacelike slice of DS.  We derive stochastic inflation via novel statements to all orders in perturbation theory and the wavefunctional approach to Quantum Field Theory.  This allows for the straightforward implementation of corrections to the original framework.