  We establish global H\"older estimates for solutions to inhomogeneous
linearized Monge-Amp\`ere equations in two dimensions with the right hand side
being the divergence of a bounded vector field. These equations arise in the
semi-geostrophic equations in meteorology and in the approximation of convex
functionals subject to a convexity constraint using fourth order Abreu type
equations. Our estimates hold under natural assumptions on the domain, boundary
data and Monge-Amp\`ere measure being bounded away from zero and infinity. They
are an affine invariant and degenerate version of global H\"older estimates by
Murthy-Stampacchia and Trudinger for second order elliptic equations in
divergence form.
