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We study homogenization for fully nonlinear uniformly parabolic equations instationary ergodic spatio-temporal media from the qualitative and quantitativeperspective. We show that under suitable hypotheses, solutions to fullynonlinear uniformly parabolic equations in spatio-temporal media homogenizealmost surely. In addition, we obtain a rate of convergence for thishomogenization in measure, assuming that the environment is strongly mixingwith a prescribed rate. A general methodology to study the stochastichomogenization of uniformly elliptic equations was introduced by Caffarelli,Souganidis, and Wang, and the rate of convergence for this homogenization wasaddressed by Caffarelli and Souganidis. We extend their approach to fullynonlinear uniformly parabolic equations, and we develop a number of newarguments to handle the parabolic structure of the problem.

On the Stochastic Homogenization of Fully Nonlinear Uniformly Parabolic Equations in Stationary Ergodic Spatio-Temporal Media