  Functional central limit theorems for random processes viewed as rough paths
were obtained in a wide range of models and settings in recent years. Each
result of this kind has described and identified the limit Brownian rough path
within the specifically suitable set-up. Taking a unified point of view, we
provide simple and exact formulae, of Green-Kubo type, that characterize the
limit Brownian rough path and demonstrate how they naturally apply in each
case.
