Stochastic dynamics of coarse-grained quantum fields in the inflationary universe.

It is shown how coarse-graining of quantum field theory in de Sitter space leads to the emergence of a classical stochastic description as an effective theory in the infra-red regime. The quantum state of the coarse-grained scalar field is found to be a highly squeezed coherent state, whose center performs a random walk on a bundle of classical trajectories.