  We consider a class of jump-diffusion processes, constrained to a polyhedral
cone $G\subset\R^n$, where the constraint vector field is constant on each face
of the boundary. The constraining mechanism corrects for ``attempts'' of the
process to jump outside the domain. Under Lipschitz continuity of the Skorohod
map \Gamma, it is known that there is a cone \mathcalC such that the image
\Gamma\phi of a deterministic linear trajectory \phi remains bounded if and
only if \dot\phi\in\mathcalC. Denoting the generator of a corresponding
unconstrained jump-diffusion by \cll, we show that a key condition for the
process to admit an invariant probability measure is that for x\in G, \cll
\id(x) belongs to a compact subset of \mathcalC^o.
