The problem of stochastic homogenization of a class of convex
Hamilton-Jacobi equations of the form
$u^\ep_t+H(x/\ep,t/\ep,Du^\ep,\om)=0$ in $\real^n\times[0,T]$ is
considered. Special attention is placed on the interplay between the use
of the Subadditive Ergodic Theorem and continuity estimates for solutions
of these equations that are independent of $H_t$, $H_x$, $\om$, $\ep$ and
the final time $T$. Moreover, an inf-sup formula for the effective
Hamiltonian is provided.

Lecture #12431

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