  We provide necessary and sufficient first order geometric conditions for the
stochastic invariance of a closed subset of R^d with respect to a
jump-diffusion under weak regularity assumptions on the coefficients. Our main
result extends the recent characterization proved in Abi Jaber, Bouchard and
Illand (2016) to jump-diffusions. We also derive an equivalent formulation in
the semimartingale framework.
