ABSTRACT
As an application of the preceding estimates, we consider a typical ergodic control of diffusions with jumps, based on the paper by Menaldi and Robin [80]. Here, we discuss ergodicity properties of a controlled jumps diffusion process reflected from the boundary of a bounded domain. The control parameters act on the drift term and on a first-order type jump density. The controlled process is generated via a Girsanov change of probability, and a long run average criterion is to be optimized. By means of the Hamilton-Jacobi-Bellman equation, an optimal stationary feedback is constructed.
