Summing inflationary logarithms in nonlinear sigma models

We consider two nonlinear sigma models on de Sitter background which involve the same derivative interactions as quantum gravity but without gauge issue. The first model contains only a single field, can be reduced to free theory by local field redefinition; second fields and cannot so reduced. Loop corrections in both produce large temporal spatial logarithms cause perturbation break down at late times distances. Many of these derive from "tail" part propagator summed using variant Starobinsky's stochastic formalism involving curvature-dependent effective potential. remaining ultraviolet renormalization group based special class renormalizations. Explicit results are derived 1-loop 2-loop orders.