Global Monge-Ampere equation with asymptotically periodic data

Let $u$ be a convex solution to $\det (D^{2}u)=f$ in ${\mathbb{R}}^n$ where $f\in C^{1,\alpha}(\mathbb R^n)$isasymptoticallyclosetoaperiodicfunction$f_p$\mathrm{.}Weprovethatthedifferencebetween$u$ and a parabola is asymptotically close to a periodic function at infinity, for dimension $n\ge 3$.