  In this talk, we compare two states: the stationary state in stochastic
inflation and the ground state wave function of the universe. We already know
that, for the potential with a static field, two pictures give the same
probability distribution. Here, we go beyond this limit and assert that two
pictures indeed have deeper relations. We illustrate a simple example so that
there is a corresponding instanton if a certain field value has a non-zero
probability in the statistical side. This instanton should be complex-valued.
Furthermore, the compact manifold in the Euclidean side can be interpreted as a
coarse-graining grid size in the stochastic universe. Finally, we summarize the
recent status and possible applications.
