  Motivated by applications to probability and mathematical finance, we
consider a parabolic partial differential equation on a half-space whose
coefficients are suitably Holder continuous and allowed to grow linearly in the
spatial variable and which become degenerate along the boundary of the
half-space. We establish existence and uniqueness of solutions in weighted
Holder spaces which incorporate both the degeneracy at the boundary and the
unboundedness of the coefficients. In our companion article [arXiv:1211.4636],
we apply the main result of this article to show that the martingale problem
associated with a degenerate-elliptic partial differential operator is
well-posed in the sense of Stroock and Varadhan.
