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In this article, we establish a viscosity method for random homogenization of an obstacle problem with nondivergence structure. We study the asymptotic behavior of the viscosity solutionuε{u}_{\varepsilon }of fully nonlinear equations in a perforated domain with the stationary ergodic condition. By capturing the behavior of the homogeneous solution, analyzing the characters of the corresponding obstacle problem, and finding the capacity-like quantity through the construction of appropriate barriers, we prove that the limit profileuuofuε{u}_{\varepsilon }satisfies a homogenized equation without obstacles.

Viscosity method for random homogenization of fully nonlinear elliptic equations with highly oscillating obstacles