  I propose the Langevin equation for 3-geometries in the Ashtekar's formalism
to describe 4D Euclidean quantum gravity, in the sense that the corresponding
Fokker-Planck hamiltonian recovers the hamiltonian in 4D quantum gravity
exactly. The stochastic time corresponds to the Euclidean time in the gauge,
N=1 and $N^i=0$. In this approach, the time evolution in 4D quantum gravity is
understood as a stochastic process where the quantum fluctuation of ` ` triad
\rq\rq is characterized by the curvature at the one unit time step before. The
lattice regularization of 4D quantum gravity is presented in this context.
