  We study the ergodic control problem for a class of jump diffusions in
$\mathbb{R}^d$, which are controlled through the drift with bounded controls.
The Levy measure is finite, but has no particular structure; it can be
anisotropic and singular. Moreover, there is no blanket ergodicity assumption
for the controlled process. Unstable behavior is `discouraged' by the running
cost which satisfies a mild coercive hypothesis (i.e., is near-monotone). We
first study the problem in its weak formulation as an optimization problem on
the space of infinitesimal ergodic occupation measures, and derive the
Hamilton-Jacobi-Bellman equation under minimal assumptions on the parameters,
including verification of optimality results, using only analytical arguments.
We also examine the regularity of invariant measures. Then, we address the jump
diffusion model, and obtain a complete characterization of optimality.
