Ergodic control of jump diffusions in Rd under a near-monotone cost assumption

We study the ergodic control problem for jump diffusion processes over R^d. Neither the running cost, nor the data are assumed to be bounded. However, the Levy measure is assumed to be locally compactly supported. We follow the vanishing discount approach and derive the HJB equation for the ergodic criterion by taking the limit of the HJB equation for the discounted criterion, as the discount factor approaches zero. In this manner, optimality over all stationary policies is established.