  We study homogenization for fully nonlinear uniformly parabolic equations in
stationary ergodic spatio-temporal media from the qualitative and quantitative
perspective. We show that under suitable hypotheses, solutions to fully
nonlinear uniformly parabolic equations in spatio-temporal media homogenize
almost surely. In addition, we obtain a rate of convergence for this
homogenization in measure, assuming that the environment is strongly mixing
with a prescribed rate. A general methodology to study the stochastic
homogenization of uniformly elliptic equations was introduced by Caffarelli,
Souganidis, and Wang, and the rate of convergence for this homogenization was
addressed by Caffarelli and Souganidis. We extend their approach to fully
nonlinear uniformly parabolic equations, and we develop a number of new
arguments to handle the parabolic structure of the problem.
